| # |
ODE |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
x^{\prime \prime }+8 x^{\prime }+15 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
x^{\prime \prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (3 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+25 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \begin{align*}
x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=3 t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+8 x&={\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
x^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.279 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= -13 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&={\mathrm e}^{2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=t \,{\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=6 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.172 |
|
| \begin{align*}
x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \begin{align*}
t x^{\prime \prime }+\left (-2+t \right ) x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.185 |
|
| \begin{align*}
t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.183 |
|
| \begin{align*}
t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.185 |
|
| \begin{align*}
t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.193 |
|
| \begin{align*}
t x^{\prime \prime }-2 x^{\prime }+t x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.190 |
|
| \begin{align*}
t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x&=0 \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.215 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=1+\delta \left (-2+t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=t +\delta \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=2 \delta \left (t -\pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.568 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=\delta \left (t \right )-\delta \left (-2+t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+9 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+8 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+8 x&=f \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\prime \prime }+\omega ^{2} y&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.784 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.998 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.295 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
11.090 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.904 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.937 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.374 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.424 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.347 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
y^{\prime \prime }+y&=t^{2} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+7 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=t^{3} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.206 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (t_{0} \right ) &= 1 \\
y^{\prime }\left (t_{0} \right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
y^{\prime \prime }+y&=t \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.130 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=1+{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.278 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.030 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.455 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.050 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.399 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.007 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )+\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (t -1\right )-\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.726 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
-2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
3 y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \begin{align*}
y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
-y+y^{\prime }&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
-y+y^{\prime }&=5 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=36 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
y^{\prime \prime }-y&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.423 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= A \\
y^{\prime }\left (0\right ) &= B \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime }+2 y&=2 \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.233 |
|
| \begin{align*}
-2 y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) {\mathrm e}^{-2+t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.687 |
|
| \begin{align*}
-y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.116 |
|
| \begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.688 |
|
| \begin{align*}
y^{\prime }-3 y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.844 |
|
| \begin{align*}
y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \\
y \left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
29.639 |
|
| \begin{align*}
y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.685 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=1-3 \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.611 |
|
| \begin{align*}
y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.548 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.437 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=5 \operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.796 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.310 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.946 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -5\right ) \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \begin{align*}
-2 y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.149 |
|
| \begin{align*}
y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| \begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.499 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.723 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.485 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.980 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.709 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.122 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.006 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=60 \cos \left (3 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=8 \sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.246 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.145 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.522 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 15 \\
y^{\prime }\left (0\right ) &= -6 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.504 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 t^{2} \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\left (2 t^{2}+t +1\right ) \delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.124 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \begin{align*}
2 y+y^{\prime }&=2 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.921 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2} \\
q \left (0\right ) &= 0 \\
q^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.264 |
|
| \begin{align*}
y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| \begin{align*}
y^{\prime }+2 y&=0 \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 11 \\
y^{\prime }\left (0\right ) &= 28 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y}{4}&=0 \\
y \left (0\right ) &= 12 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \\
y \left (0\right ) &= {\frac {16}{5}} \\
y^{\prime }\left (0\right ) &= {\frac {31}{5}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.233 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= {\frac {7}{2}} \\
y^{\prime }\left (0\right ) &= -10 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= {\frac {81}{10}} \\
y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \\
y \left (0\right ) &= -25 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {63}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
y \left (4\right ) &= -3 \\
y^{\prime }\left (4\right ) &= -17 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \begin{align*}
y^{\prime }-6 y&=0 \\
y \left (-1\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100 \\
y \left (2\right ) &= -4 \\
y^{\prime }\left (2\right ) &= 14 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.655 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\
y \left (\frac {3}{2}\right ) &= 4 \\
y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \\
y \left (0\right ) &= {\frac {19}{12}} \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.934 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
10.649 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=\left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
14.021 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
14.714 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.542 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
14.829 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \\
y \left (1\right ) &= 1+\cos \left (2\right ) \\
y^{\prime }\left (1\right ) &= 4-2 \sin \left (2\right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.694 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.492 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.133 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.671 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.083 |
|
| \begin{align*}
4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.146 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
17.057 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
11.540 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
14.323 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
y^{\prime \prime }-y&=t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
L i^{\prime }+R i&=E_{0} \operatorname {Heaviside}\left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.888 |
|
| \begin{align*}
L i^{\prime }+R i&=E_{0} \delta \left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
L i^{\prime }+R i&=E_{0} \sin \left (\omega t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-5 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.412 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.723 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.318 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+3 y&=2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+2 y&=t \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
i^{\prime \prime }+2 i^{\prime }+3 i&=\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \\
i \left (0\right ) &= 8 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
46.193 |
|
| \begin{align*}
-y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \begin{align*}
y+2 y^{\prime }&=0 \\
y \left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
y^{\prime }+6 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.280 |
|
| \begin{align*}
-y+y^{\prime }&=2 \cos \left (5 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.427 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.420 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| \begin{align*}
y+y^{\prime }&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-4 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \begin{align*}
-y+y^{\prime }&=1+{\mathrm e}^{t} t \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.463 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=1+t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+20 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.374 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.320 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.345 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.571 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.805 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
11.193 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.361 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=1-\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
24.244 |
|
| \begin{align*}
y+y^{\prime }&=t \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| \begin{align*}
-y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.773 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.019 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.596 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right )+t \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
y^{\prime }-3 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.401 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.177 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.740 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.405 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.368 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.243 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.022 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.225 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.237 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.816 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
19.246 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
17.648 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.357 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
y \left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
2.079 |
|
| \begin{align*}
y^{\prime }-t y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
1.207 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| \begin{align*}
y^{\prime } t +y&=0 \\
y \left (1\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| \begin{align*}
y^{\prime } t +y&=\sin \left (t \right ) \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
2.795 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
y \left (1\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| \begin{align*}
t^{2} y+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.935 |
|
| \begin{align*}
\left (a t +1\right ) y^{\prime }+y&=t \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.618 |
|
| \begin{align*}
y^{\prime }+\left (a t +b t \right ) y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| \begin{align*}
y^{\prime }+\left (a t +b t \right ) y&=0 \\
y \left (-3\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.003 |
|
| \begin{align*}
x^{\prime }+5 x&=\operatorname {Heaviside}\left (-2+t \right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.157 |
|
| \begin{align*}
x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-6 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&={\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
20.177 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
x^{\prime \prime }-2 x&=1 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x^{\prime }&=2 x+\operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.659 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \begin{align*}
x^{\prime }&=x-2 \operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \begin{align*}
x^{\prime }&=-x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.694 |
|
| \begin{align*}
x^{\prime \prime }+\pi ^{2} x&=\pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.470 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=1-\operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.056 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
x^{\prime }+3 x&=\delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.485 |
|
| \begin{align*}
x^{\prime \prime }-x&=\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.003 |
|
| \begin{align*}
x^{\prime \prime }+x&=\delta \left (-2+t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.118 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\delta \left (-2+t \right )-\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.158 |
|
| \begin{align*}
x^{\prime \prime }+x&=3 \delta \left (t -2 \pi \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.208 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.254 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
y+y^{\prime }&=2 \sin \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=9 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.031 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
8.517 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
9.579 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
18.013 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
12.460 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.653 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.750 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+37 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y^{\prime \prime }-20 y^{\prime }+51 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -14 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \begin{align*}
4 y^{\prime \prime }+40 y^{\prime }+101 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+34 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
y^{\prime \prime }\left (0\right ) &= -20 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= -24 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
y^{\prime \prime \prime }\left (0\right ) &= 19 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \begin{align*}
4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= -{\frac {2}{13}} \\
y^{\prime }\left (0\right ) &= {\frac {1}{13}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \begin{align*}
y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2} \\
y \left (0\right ) &= -12 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.086 |
|
| \begin{align*}
-2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.684 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.430 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.694 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.532 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (-2+t \right ) \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.980 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \\
y \left (0\right ) &= {\frac {3}{4}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+5 y&=25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
16.567 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
19.614 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\
y \left (0\right ) &= -6 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
7.609 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
13.267 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
7.053 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.389 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.908 |
|
| \begin{align*}
y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
21.424 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.003 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+29 y&=5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.128 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.623 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.138 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.871 |
|
| \begin{align*}
10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
Q \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.793 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.310 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.888 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.206 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=18 t \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=f \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.069 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
13.534 |
|
| \begin{align*}
x^{\prime \prime }+2 t x^{\prime }-4 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.474 |
|
| \begin{align*}
c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=\delta \left (t -1\right )-\delta \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.730 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \begin{align*}
2 y+y^{\prime }&=4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.206 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{x}-3 x^{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.155 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=2+x \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.150 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=2+x \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.248 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x +\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
y^{\prime }-2 y&=6 \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= {\frac {5}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.164 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=x^{2} \\
y \left (0\right ) &= {\frac {11}{4}} \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.321 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.164 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
2 y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.213 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
20.069 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
8.980 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
11.391 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.850 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.482 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
13.304 |
|
| \begin{align*}
y^{\prime }+3 y&=\delta \left (x -2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.187 |
|
| \begin{align*}
y^{\prime }-3 y&=\delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (x -2\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.908 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.164 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (-1+x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.908 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=\cos \left (x \right )+2 \delta \left (x -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.681 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\cos \left (x \right ) \delta \left (x -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.720 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \\
y \left (0\right ) &= 11 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.161 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.284 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=13 \operatorname {Heaviside}\left (t -4\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
21.211 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\cos \left (2 t \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.376 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.095 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+9 y&=20 \operatorname {Heaviside}\left (-2+t \right ) \sin \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
14.492 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.974 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.299 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.266 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.363 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
23.967 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&={\mathrm e}^{-2 t} \sin \left (4 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (-2+t \right ) \sin \left (-8+4 t \right ) \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
18.013 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
29.473 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+3 y&=\left (1-\operatorname {Heaviside}\left (-2+t \right )\right ) {\mathrm e}^{\frac {1}{5}-\frac {t}{10}} \sin \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
30.319 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| \begin{align*}
y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{3} \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
3 y+y^{\prime }&=\operatorname {Heaviside}\left (t -4\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.389 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=t^{3} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=7 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.271 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.934 |
|
| \begin{align*}
y^{\prime \prime \prime }-27 y&={\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime }+t y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=27 t^{3} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t^{2} {\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+17 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.000 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.406 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
y^{\prime \prime }+4 y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.319 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.299 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.588 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.717 |
|
| \begin{align*}
y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
17.288 |
|
| \begin{align*}
y^{\prime }&=3 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
y^{\prime }&=\delta \left (-2+t \right )-\delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
y^{\prime \prime }&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \begin{align*}
y^{\prime \prime }&=\delta \left (t -1\right )-\delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| \begin{align*}
y^{\prime }+2 y&=4 \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.956 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t \right )+\delta \left (t -\pi \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
y^{\prime \prime }+y&=-2 \delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.371 |
|
| \begin{align*}
3 y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.053 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.912 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.365 |
|
| \begin{align*}
y^{\prime \prime }-16 y&=\delta \left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.222 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.280 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.191 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\delta \left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.634 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \begin{align*}
y^{\prime \prime \prime }+9 y^{\prime }&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.104 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.702 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\
x \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\
x \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
x^{\prime }+x&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \begin{align*}
x^{\prime \prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \begin{align*}
x^{\prime \prime }&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
x^{\prime \prime }&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.203 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=1 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
x^{\prime \prime }+x&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }&=12 t +2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=2 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=4 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
2 x^{\prime \prime }-2 x^{\prime }&=\left (1+t \right ) {\mathrm e}^{t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
x^{\prime \prime }+x&=2 \cos \left (t \right ) \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{t} t^{2}+7 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=t \cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 9 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.776 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right . \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.979 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.271 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.030 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.167 |
|
| \begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.815 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.032 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.090 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.355 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 12 \\
y^{\prime }\left (0\right ) &= 7 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
y^{\prime \prime \prime }\left (0\right ) &= -9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.461 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
21.529 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.011 |
|
| \begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.455 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.090 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.450 |
|
| \begin{align*}
y^{\prime \prime }-y&=-20 \delta \left (t -3\right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.239 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.409 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| \begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.356 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.144 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.631 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.573 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.545 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.550 |
|
| \begin{align*}
y^{\prime \prime }+w^{2} y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.644 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.546 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.913 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| \begin{align*}
\frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
\frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime }+y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=3 x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-x} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.607 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
0.685 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.864 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{2 t} t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=t^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.523 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.418 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.639 |
|
| \begin{align*}
x^{\prime }+x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| \begin{align*}
x^{\prime }+x&=t \\
x \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+3 x&=1 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
x^{\prime }-x&=\operatorname {Heaviside}\left (t -a \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
39.106 |
|
| \begin{align*}
x^{\prime }+x&=\operatorname {Heaviside}\left (t -a \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
27.333 |
|
| \begin{align*}
x^{\prime }-x&=k \delta \left (t \right ) \\
x \left (0\right ) &= a \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
x^{\prime \prime }+x&=g \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| \begin{align*}
x^{\prime \prime }&=\delta \left (-t +a \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.230 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (\pi \right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{5 t} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \begin{align*}
y^{\prime }+2 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
y^{\prime }+b y&=1 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.244 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=t \\
y \left (0\right ) &= -3 \\
y \left (1\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.267 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.823 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.777 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
11.019 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
10.108 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.365 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
y^{\prime \prime }+n^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= k \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= {\frac {3}{2}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.255 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
y^{\prime \prime \prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= -4 \\
y^{\prime \prime \prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\
y \left (0\right ) &= {\frac {7}{9}} \\
y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.494 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 t -8 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
y \left (\pi \right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.754 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 t^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.884 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.390 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
1.365 |
|
| \begin{align*}
y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
y^{\prime }+2 y&=2 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.267 |
|
| \begin{align*}
y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y^{\prime }+5 y&=0 \\
y \left (1\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (t -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.409 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.286 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.739 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=12 t \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 20 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.789 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.429 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.437 |
|
| \begin{align*}
y^{\prime }+2 y&=5 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.428 |
|
| \begin{align*}
y^{\prime \prime }+y&=3 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.655 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.565 |
|
| \begin{align*}
y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.235 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=4 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \begin{align*}
y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
y^{\prime \prime }-y&=6 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=-3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=2 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.604 |
|
| \begin{align*}
y^{\prime \prime \prime }-27 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 6 \\
y^{\prime \prime }\left (0\right ) &= 18 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+18 y&=54 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.792 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=20 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 18 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+26 y&=37 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=-1 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.918 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=-1 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.120 |
|
| \begin{align*}
y^{\prime }-3 y&=2 \,{\mathrm e}^{t} \\
y \left (1\right ) &= {\mathrm e}^{3}-{\mathrm e} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=27 t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=25 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.032 |
|
| \begin{align*}
y^{\prime \prime }+13 y^{\prime }+36 y&=10-72 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+21 y&=21 t^{2}+t +13 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| \begin{align*}
4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=12 \sinh \left (t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.359 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.441 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=39 \,{\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.031 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=18 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 13 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.125 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y&=-12 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= -8 \\
y^{\prime }\left (0\right ) &= 24 \\
y^{\prime \prime }\left (0\right ) &= -46 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.125 |
|
| \begin{align*}
y^{\prime \prime }-y&=2 t^{2}+2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=13 t +17+40 \sin \left (t \right ) \\
y \left (0\right ) &= 30 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.579 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.861 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \sin \left (x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.803 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y&=x^{2}-4 \cos \left (3 x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.569 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.848 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime }+2 y&=-2 x^{4}+x^{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.926 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.293 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=3 x -6 \\
y \left (0\right ) &= {\frac {1}{3}} \\
y^{\prime }\left (0\right ) &= {\frac {4}{3}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \begin{align*}
y^{\left (5\right )}&=120 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 6 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 24 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| \begin{align*}
2 y^{\prime }+y&={\mathrm e}^{x} \\
y \left (2\right ) &= \frac {4 \,{\mathrm e}^{2}}{3} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.215 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2} \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi ^{2}}{4} \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \pi \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| \begin{align*}
y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| \begin{align*}
y^{\prime }-4 y&=1 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.384 |
|
| \begin{align*}
y^{\prime }-4 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.097 |
|
| \begin{align*}
y^{\prime }+a y&={\mathrm e}^{-a t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
y^{\prime }+2 y&=3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \begin{align*}
y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.681 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.603 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.581 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.129 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.136 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=9 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.129 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.145 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=150 t \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.723 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.130 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.723 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.654 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=2 \cos \left (t \right )+\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| \begin{align*}
y^{\prime \prime }+y&=4 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.605 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.421 |
|
| \begin{align*}
y^{\prime \prime }-3 y&=4 t^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.604 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=32 t \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.457 |
|
| \begin{align*}
t y^{\prime \prime }+\left (1+t \right ) y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.691 |
|
| \begin{align*}
t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.884 |
|
| \begin{align*}
t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.083 |
|
| \begin{align*}
t y^{\prime \prime }-4 y^{\prime }+t y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.777 |
|
| \begin{align*}
t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.841 |
|
| \begin{align*}
-t y^{\prime \prime }+\left (-2+t \right ) y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.944 |
|
| \begin{align*}
-t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.141 |
|
| \begin{align*}
t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.976 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.590 |
|
| \begin{align*}
t y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } t +y&=0 \\
\end{align*}
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
0.190 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.991 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
15.547 |
|
| \begin{align*}
y^{\prime \prime }-a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
20.860 |
|
| \begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
13.423 |
|
| \begin{align*}
y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
15.424 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
36.413 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
5.201 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
22.065 |
|
| \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
19.779 |
|
| \begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
22.536 |
|
| \begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\
y \left (\pi \right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
16.636 |
|
| \begin{align*}
y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
17.359 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
14.302 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
5.144 |
|
| \begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
9.180 |
|
| \begin{align*}
y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
14.855 |
|
| \begin{align*}
y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
25.700 |
|
| \begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
16.961 |
|
| \begin{align*}
y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
52.352 |
|
| \begin{align*}
3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
26.618 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
14.125 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
28.164 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
26.154 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.223 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
15.078 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
19.329 |
|
| \begin{align*}
y^{\prime }+2 y&=\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.425 |
|
| \begin{align*}
y^{\prime }-3 y&=3+\delta \left (-2+t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.121 |
|
| \begin{align*}
y^{\prime }-4 y&=\delta \left (t -4\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.951 |
|
| \begin{align*}
y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
16.848 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.609 |
|
| \begin{align*}
y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
21.572 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
22.967 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
13.474 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
14.003 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
15.641 |
|
| \begin{align*}
y^{\prime }-3 y&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
16.728 |
|
| \begin{align*}
y^{\prime }+4 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.920 |
|
| \begin{align*}
y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.675 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.986 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.478 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.341 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.789 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.853 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.864 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.594 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{a t} \\
y \left (0\right ) &= A \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.039 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{a t} \\
y \left (0\right ) &= A \\
y^{\prime }\left (0\right ) &= B \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=1 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.401 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.514 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.979 |
|
| \begin{align*}
y^{\prime }-a y&=t \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=1 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.575 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.427 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\delta \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.003 |
|
| \begin{align*}
y^{\prime \prime }+y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
y^{\prime \prime }+B y^{\prime }+C y&=\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.226 |
|
| \begin{align*}
y^{\prime \prime }+B y^{\prime }+C y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.481 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (t \right )+\delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.792 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.016 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.138 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=12 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=8 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.102 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.546 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.908 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-t} \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.151 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.171 |
|
| \begin{align*}
x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\
x \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.733 |
|
| \begin{align*}
x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.724 |
|
| \begin{align*}
x^{\prime }+x&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.175 |
|
| \begin{align*}
x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\
x \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.333 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.625 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=1 \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.721 |
|
| \begin{align*}
x^{\prime \prime }-5 x^{\prime }+6 x&=12 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }-1&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{3}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.075 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+1&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&=2 t^{2}+1 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.381 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }-3 x&=3 t^{2}+7 t +3 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.385 |
|
| \begin{align*}
x^{\prime \prime }-7 x^{\prime }&=-14 t -5 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.996 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }&=6 t^{2}+6 t -3 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.862 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -{\frac {1}{36}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.302 |
|
| \begin{align*}
x^{\prime \prime }+x&=2 \,{\mathrm e}^{t} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.157 |
|
| \begin{align*}
7 x^{\prime \prime }+14 x^{\prime }&=\left (t -\frac {1}{4}\right ) {\mathrm e}^{-2 t} \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -{\frac {1}{56}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.634 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=\left (t -1\right ) {\mathrm e}^{2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.269 |
|
| \begin{align*}
4 x^{\prime \prime }-4 x^{\prime }+x&={\mathrm e}^{\frac {t}{2}} \\
x \left (0\right ) &= -2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.276 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-t}+{\mathrm e}^{-2 t} \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-6 x&=6 \,{\mathrm e}^{3 t}+2 \,{\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {4}{5}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.769 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=t^{2} {\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.671 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.257 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=18 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.976 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=4 \cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{8}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.855 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+3 x&=t \cos \left (t \right ) \\
x \left (0\right ) &= -{\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.866 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+10 x&=\cos \left (3 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= {\frac {18}{37}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.861 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+5 x&=2 \,{\mathrm e}^{2 t} \left (\sin \left (t \right )+\cos \left (t \right )\right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.862 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime \prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 3 \\
x^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.861 |
|
| \begin{align*}
x^{\prime \prime \prime }-x&=2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= \frac {1}{2}+\frac {\sqrt {3}}{2} \\
x^{\prime \prime }\left (0\right ) &= \frac {1}{2}-\frac {\sqrt {3}}{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.073 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-2 x&={\mathrm e}^{t} t \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= {\frac {21}{25}} \\
x^{\prime \prime }\left (0\right ) &= -{\frac {28}{25}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.815 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (t +\frac {\pi }{4}\right ) \\
x \left (0\right ) &= -{\frac {40}{17}} \\
x^{\prime }\left (0\right ) &= {\frac {24}{17}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.792 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (2 t +\frac {\pi }{4}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.825 |
|
| \begin{align*}
y^{\prime }+4 y&=1 \\
y \left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.831 |
|
| \begin{align*}
y^{\prime }-9 y&=t \\
y \left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.369 |
|
| \begin{align*}
y^{\prime }+4 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.593 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
-2 y+y^{\prime }&=1-t \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.471 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.727 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.667 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.407 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=1+t \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.387 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.795 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 3 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
35.365 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 12 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
24.964 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y&=\left \{\begin {array}{cc} 0 & 0\le t <6 \\ 2 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
30.734 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} -2 & 0\le t <3 \\ 0 & 3\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
28.523 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 2 & 5\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
37.130 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <3 \\ t +2 & 3\le t \end {array}\right . \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
56.471 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
21.364 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+24 y&=f \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
28.993 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+12 y&=f \left (t \right ) \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
20.550 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=f \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
20.645 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=f \left (t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
23.808 |
|
| \begin{align*}
y^{\prime \prime }-k^{2} y&=f \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
29.943 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
13.236 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-11 y^{\prime \prime }+18 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
32.798 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=3 \delta \left (-2+t \right )-4 \delta \left (t -5\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
26.766 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=4 \delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
19.570 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=6 \delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.637 |
|
| \begin{align*}
y^{\prime \prime }+16 y^{\prime }&=12 \delta \left (t -\frac {5 \pi }{8}\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
17.059 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=8 \delta \left (t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.979 |
|
| \begin{align*}
t^{2} y^{\prime }-2 y&=2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
187.465 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } t -4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -7 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.899 |
|
| \begin{align*}
y^{\prime \prime }-16 y^{\prime } t +32 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.472 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime } t -8 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.550 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.754 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } t -4 y&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.089 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime } t&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.966 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } t +4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.522 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime } t +16 y&=3 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.096 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.230 |
|