| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11201 |
\begin{align*}
y^{\prime \prime }-4 y&=\sinh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11202 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11203 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11204 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-b x_{1}-a x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11205 |
\begin{align*}
y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.602 |
|
| 11206 |
\begin{align*}
2+4 y^{\prime } x +x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11207 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11208 |
\begin{align*}
\left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11209 |
\begin{align*}
2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.602 |
|
| 11210 |
\begin{align*}
2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11211 |
\begin{align*}
x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 x {y^{\prime }}^{2}+x \left (x +2 y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.602 |
|
| 11212 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11213 |
\begin{align*}
y^{\prime \prime } x +x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.602 |
|
| 11214 |
\begin{align*}
y^{\prime }&=\frac {1}{2 y+3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11215 |
\begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11216 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11217 |
\begin{align*}
y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.602 |
|
| 11218 | \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.602 |
|
| 11219 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 \sin \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11220 |
\begin{align*}
y^{\prime \prime }&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11221 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\
y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| 11222 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+4 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11223 |
\begin{align*}
y^{\prime \prime }+9 y&=18 \sec \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11224 |
\begin{align*}
x^{\prime }-2 x+2 y^{\prime }&=-4 \,{\mathrm e}^{2 t} \\
2 x^{\prime }-3 x+3 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11225 |
\begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| 11226 |
\begin{align*}
x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| 11227 |
\begin{align*}
\left (4 x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| 11228 |
\begin{align*}
y^{\prime }&=3-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11229 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11230 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=x \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| 11231 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11232 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+x&=k \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11233 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| 11234 |
\begin{align*}
y^{\prime \prime } x +x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| 11235 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| 11236 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| 11237 | \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. | ✓ | ✓ | ✓ | ✓ | 0.604 |
|
| 11238 |
\begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.604 |
|
| 11239 |
\begin{align*}
y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| 11240 |
\begin{align*}
\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| 11241 |
\begin{align*}
y^{\prime }&=2 y \left (y-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| 11242 |
\begin{align*}
x_{1}^{\prime }&=25 x_{1}+12 x_{2} \\
x_{2}^{\prime }&=-18 x_{1}-5 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+13 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11243 |
\begin{align*}
x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3} \\
x_{2}^{\prime }&=5 x_{2} \\
x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11244 |
\begin{align*}
x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3} \\
x_{3}^{\prime }&=3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11245 |
\begin{align*}
2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11246 |
\begin{align*}
\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.605 |
|
| 11247 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&=0 \\
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*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11248 |
\begin{align*}
8 y^{\prime \prime }-y&=x \,{\mathrm e}^{-\frac {x}{2}} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11249 |
\begin{align*}
f^{\prime \prime }+6 f^{\prime }+9 f&={\mathrm e}^{-t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= \lambda \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11250 |
\begin{align*}
z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11251 |
\begin{align*}
2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}&={\mathrm e}^{x} \\
y_{1}^{\prime }+3 y_{1}+y_{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11252 |
\begin{align*}
-\left (-a^{2} x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11253 |
\begin{align*}
x^{\prime }&=3 x+2 y+4 z \\
y^{\prime }&=2 x+2 z \\
z^{\prime }&=4 x+2 y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11254 |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.605 |
|
| 11255 |
\begin{align*}
4 y+y^{\prime \prime }&=\csc \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11256 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11257 | \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=9 x^{2}-12 x +2 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.605 |
|
| 11258 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11259 |
\begin{align*}
y^{\prime }&={\mathrm e}^{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11260 |
\begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }-21 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11261 |
\begin{align*}
t^{2} y^{\prime \prime }+3 t \left (1+3 t \right ) y^{\prime }+\left (-t^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11262 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+c y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| 11263 |
\begin{align*}
8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11264 |
\begin{align*}
4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11265 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=x \left (-x^{2}+1\right ) \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.606 |
|
| 11266 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11267 |
\begin{align*}
-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11268 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11269 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.606 |
|
| 11270 |
\begin{align*}
y^{\prime \prime }-25 y&=\frac {1}{1-{\mathrm e}^{5 t}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11271 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11272 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=16 \,{\mathrm e}^{-x}+9 x -6 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11273 |
\begin{align*}
x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| 11274 |
\begin{align*}
\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| 11275 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+6 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=6 x_{1}+x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| 11276 | \begin{align*}
y^{\prime \prime }+9 y&=\sin \left (2 x \right )+\cos \left (2 x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.607 |
|
| 11277 |
\begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| 11278 |
\begin{align*}
x^{\prime }&=x-y+2 z \\
y^{\prime }&=-x+y+2 z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| 11279 |
\begin{align*}
8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| 11280 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| 11281 |
\begin{align*}
x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11282 |
\begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11283 |
\begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11284 |
\begin{align*}
x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11285 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11286 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11287 |
\begin{align*}
y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.608 |
|
| 11288 |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11289 |
\begin{align*}
x^{\prime }&=7 x-5 y \\
y^{\prime }&=10 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11290 |
\begin{align*}
x^{\prime }&=-5 y \\
y^{\prime }&=x+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11291 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11292 |
\begin{align*}
8 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11293 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| 11294 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 11295 | \begin{align*}
\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=\left (3 x -1\right )^{2} {\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 0.609 |
|
| 11296 |
\begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 11297 |
\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. |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 11298 |
\begin{align*}
x^{\prime }&=-2 x+y+t \\
y^{\prime }&=-4 x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 11299 |
\begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| 11300 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -20 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.609 |
|