| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1(a) |
\begin{align*}
y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(b) |
\begin{align*}
x^{2} y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(c) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 1(d) |
\begin{align*}
x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(e) |
\begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(f) |
\begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(g) |
\begin{align*}
y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| Problem 1(h) |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(i) |
\begin{align*}
y^{\prime }&=\ln \left (y x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 2(a) |
\begin{align*}
x \left (y+1\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1(a) |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 1(b) |
\begin{align*}
y^{\prime \prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 1(c) |
\begin{align*}
y^{\prime \prime }+y y^{\prime }&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 1(d) |
\begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }&=2 x^{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 1(e) |
\begin{align*}
y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 1(f) |
\begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 1(g) |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(h) |
\begin{align*}
y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 1(i) |
\begin{align*}
y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(j) |
\begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 1(k) |
\begin{align*}
5 y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(L) |
\begin{align*}
{y^{\prime }}^{2} \sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(m) |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 1(n) |
\begin{align*}
y^{\prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(o) |
\begin{align*}
x^{2} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(a) |
\begin{align*}
y^{\prime \prime }&=x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(b) |
\begin{align*}
y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2}&=\sin \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 2(c) | \begin{align*}
{y^{\prime }}^{2}+x y {y^{\prime }}^{2}&=\ln \left (x \right ) \\
\end{align*} | ✗ | ✗ | ✗ | ✗ |
|
| Problem 2(d) |
\begin{align*}
\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 2(e) |
\begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=y x \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 2(f) |
\begin{align*}
y y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 2(h) |
\begin{align*}
{y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 3(a) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(b) |
\begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(c) |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(d) |
\begin{align*}
3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(a) |
\begin{align*}
\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right )&=x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 5(b) |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right )&=0 \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| Problem 5(c) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| Problem 5(d) |
\begin{align*}
x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right )&=\sinh \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 5(e) |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 5(f) |
\begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y&=\tan \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 10 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 13 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 15 |
\begin{align*}
y^{\prime \prime }+\frac {k x}{y^{4}}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
|
| Problem 18(a) |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(b) |
\begin{align*}
x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| Problem 18(c) | \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x&=2 x \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
|
| Problem 18(d) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=1-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(e) |
\begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(f) |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 18(g) |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(h) |
\begin{align*}
\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 18(i) |
\begin{align*}
x y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(j) |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(k) |
\begin{align*}
-\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 18(L) |
\begin{align*}
x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 19(a) |
\begin{align*}
x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 19(b) |
\begin{align*}
\frac {x y^{\prime \prime }}{y+1}+\frac {y y^{\prime }-{y^{\prime }}^{2} x +y^{\prime }}{\left (y+1\right )^{2}}&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 19(c) |
\begin{align*}
\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| Problem 19(d) |
\begin{align*}
y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 19(e) |
\begin{align*}
\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 19(f) |
\begin{align*}
\left (\cos \left (y\right )-\sin \left (y\right ) y\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right )&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| Problem 20(a) |
\begin{align*}
y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 20(b) |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 20(c) |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (x +2\right ) y}{x^{2} \left (x +1\right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 20(d) |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 20(e) | \begin{align*}
\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x}&=3 x \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
|
| Problem 20(f) |
\begin{align*}
\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| Problem 20(g) |
\begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 20(h) |
\begin{align*}
y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (8+4 x \right ) y&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 2 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 7 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 8 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 9 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 10 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 11 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 12 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 14 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 15 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 16 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 17 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 18 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 19 | \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. | ✓ | ✓ | ✓ | ✓ |
|
| Problem 20 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 21 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 22 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 23 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 24 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 25 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 26 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 27 |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 2(a) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(b) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(c) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(d) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(e) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(f) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(g) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(h) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(i) |
\begin{align*}
y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(i)[j] |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(j)[k] |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(k)[l] |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(m) |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(l)[n] |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(a) |
\begin{align*}
y+y^{\prime }&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(b) |
\begin{align*}
-2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(c) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(d) | \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. | ✓ | ✓ | ✓ | ✓ |
|
| Problem 3(e) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(f) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(g) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(h) |
\begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right ) \\
y \left (0\right ) &= {\frac {3}{4}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(i) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(j) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(a) |
\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. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 4(b) |
\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. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 4(c) |
\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. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 4(d) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(e) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(a) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(b) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(c) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(d) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(e) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(f) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6(a) |
\begin{align*}
10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\
Q \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13(a) | \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. | ✓ | ✓ | ✓ | ✓ |
|
| Problem 13(b) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13(c) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 13(d) |
\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. |
✓ |
✓ |
✓ |
✗ |
|
| Problem 14(a) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| Problem 14(b) |
\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. |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1(a) |
\begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=t^{7} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(b) |
\begin{align*}
t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y&=\ln \left (t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 1(c) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 1(d) |
\begin{align*}
y^{\prime \prime }+t y^{\prime }-\ln \left (t \right ) y&=\cos \left (2 t \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| Problem 1(e) |
\begin{align*}
t^{3} y^{\prime \prime }-2 t y^{\prime }+y&=t^{4} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
|
| Problem 2(a) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(b) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(c) |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-7 y&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(d) |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(e) |
\begin{align*}
3 y^{\prime \prime }+5 y^{\prime }-2 y&=3 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 2(f) |
\begin{align*}
y^{\prime \prime \prime }&=2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(a) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=3 x \left (t \right )-4 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(b) |
\begin{align*}
x^{\prime }\left (t \right )&=\frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4} \\
y^{\prime }\left (t \right )&=\frac {x \left (t \right )}{2}-\frac {3 y \left (t \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(c) |
\begin{align*}
x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )&=0 \\
y^{\prime }\left (t \right )+y \left (t \right )-x \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(d) |
\begin{align*}
x^{\prime }\left (t \right )+5 x \left (t \right )-2 y \left (t \right )&=0 \\
2 x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(e) |
\begin{align*}
x^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right )&=0 \\
y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(f) |
\begin{align*}
x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right )&=0 \\
x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )&=0 \\
z^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )-3 z \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(g) | \begin{align*}
x^{\prime }\left (t \right )&=-\frac {x \left (t \right )}{2}+2 y \left (t \right )-3 z \left (t \right ) \\
y^{\prime }\left (t \right )&=y \left (t \right )-\frac {z \left (t \right )}{2} \\
z^{\prime }\left (t \right )&=-2 x \left (t \right )+z \left (t \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 4(a) |
\begin{align*}
x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=y \left (t \right ) \\
x^{\prime }\left (t \right )-y^{\prime }\left (t \right )&=x \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(b) |
\begin{align*}
x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )&=t \\
x^{\prime }\left (t \right )-y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(c) |
\begin{align*}
x^{\prime }\left (t \right )-y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )-t \\
2 x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right )&=2 x \left (t \right )+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(d) |
\begin{align*}
2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )&=t \\
3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )&=y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(e) |
\begin{align*}
5 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \\
3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(f) |
\begin{align*}
x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right )&=0 \\
2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )&=t +y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(g) |
\begin{align*}
3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )&=\sin \left (t \right ) \\
x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 3(a) |
\begin{align*}
x^{\prime }\left (t \right )&=-4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t} \\
y^{\prime }\left (t \right )&=-5 x \left (t \right )+2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(b) |
\begin{align*}
x^{\prime }\left (t \right )&=-7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t} \\
y^{\prime }\left (t \right )&=-12 x \left (t \right )+5 y \left (t \right )+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(c) |
\begin{align*}
x^{\prime }\left (t \right )&=-7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t} \\
y^{\prime }\left (t \right )&=-10 x \left (t \right )+9 y \left (t \right )+37 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 3(d) |
\begin{align*}
x^{\prime }\left (t \right )&=-14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right ) \\
y^{\prime }\left (t \right )&=-6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(a) |
\begin{align*}
x^{\prime }\left (t \right )&=2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right ) \\
y^{\prime }\left (t \right )&=4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right ) \\
z^{\prime }\left (t \right )&=-x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(b) |
\begin{align*}
x^{\prime }\left (t \right )&=2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t} \\
y^{\prime }\left (t \right )&=6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t} \\
z^{\prime }\left (t \right )&=-x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(c) |
\begin{align*}
x^{\prime }\left (t \right )&=-2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ) \\
y^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ) \\
z^{\prime }\left (t \right )&=-4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 4(d) |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right ) \\
y^{\prime }\left (t \right )&=x \left (t \right )-y \left (t \right )+2 z \left (t \right )+2 \,{\mathrm e}^{-t} \\
z^{\prime }\left (t \right )&=-2 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(a) |
\begin{align*}
x^{\prime }\left (t \right )&=7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t} \\
y^{\prime }\left (t \right )&=-4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(b) |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right ) \\
y^{\prime }\left (t \right )&=9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(c) |
\begin{align*}
x^{\prime }\left (t \right )&=7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t} \\
y^{\prime }\left (t \right )&=3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 5(d) |
\begin{align*}
x^{\prime }\left (t \right )&=-7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t} \\
y^{\prime }\left (t \right )&=-5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6(a) |
\begin{align*}
x^{\prime }\left (t \right )&=-3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ) \\
y^{\prime }\left (t \right )&=2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t} \\
z^{\prime }\left (t \right )&=5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
|
| Problem 6(b) |
\begin{align*}
x^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right ) \\
y^{\prime }\left (t \right )&=y \left (t \right )+z \left (t \right )-10 \cos \left (t \right ) \\
z^{\prime }\left (t \right )&=x \left (t \right )+z \left (t \right )+2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6(c) |
\begin{align*}
x^{\prime }\left (t \right )&=-3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right ) \\
y^{\prime }\left (t \right )&=x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right ) \\
z^{\prime }\left (t \right )&=-3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 6(d) |
\begin{align*}
x^{\prime }\left (t \right )&=-3 x \left (t \right )+y \left (t \right )-3 z \left (t \right )+2 \,{\mathrm e}^{t} \\
y^{\prime }\left (t \right )&=4 x \left (t \right )-y \left (t \right )+2 z \left (t \right )+4 \,{\mathrm e}^{t} \\
z^{\prime }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )+4 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 1(a) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right ) \\
y^{\prime }\left (t \right )&=19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| Problem 1(b) |
\begin{align*}
x^{\prime }\left (t \right )&=9 x \left (t \right )-3 y \left (t \right )-6 t \\
y^{\prime }\left (t \right )&=-x \left (t \right )+11 y \left (t \right )+10 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|