| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {2+x}} \\
y \left (2\right ) &= -1 \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime }&=\frac {10}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime }&=\cos \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
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| 9 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 10 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime }&=y-\sin \left (x \right ) \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
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| 9 |
\begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
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| 11 |
\begin{align*}
y^{\prime }&=2 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
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| 12 |
\begin{align*}
y^{\prime }&=\ln \left (y\right ) x \\
\end{align*} |
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| 13 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
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| 14 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 17 |
\begin{align*}
y y^{\prime }&=-1+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
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| 18 |
\begin{align*}
y y^{\prime }&=-1+x \\
y \left (1\right ) &= 0 \\
\end{align*} |
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| 19 |
\begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 20 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) y \\
\end{align*} |
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| 4 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
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| 5 |
\begin{align*}
2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=3 \sqrt {y x} \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime }&=4 \left (y x \right )^{{1}/{3}} \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime }&=2 x \sec \left (y\right ) \\
\end{align*} |
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| 9 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
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| 10 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (1+y\right )^{2} \\
\end{align*} |
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| 11 |
\begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
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| 12 |
\begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
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| 14 |
\begin{align*}
y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\
\end{align*} |
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| 15 |
\begin{align*}
y^{\prime }&=\frac {\left (-1+x \right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\
\end{align*} |
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| 16 |
\begin{align*}
\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\
\end{align*} |
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| 17 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
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| 18 |
\begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\
\end{align*} |
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| 19 | \begin{align*}
y^{\prime }&={\mathrm e}^{x} y \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 20 |
\begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| 21 |
\begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
✓ |
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| 22 |
\begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
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| 23 |
\begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
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| 24 |
\begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
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| 25 |
\begin{align*}
-y+y^{\prime } x&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
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| 26 |
\begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
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| 27 |
\begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
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| 28 |
\begin{align*}
2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\
y \left (4\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
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| 2 |
\begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
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| 3 |
\begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime } x +2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
✓ |
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| 6 |
\begin{align*}
2 y^{\prime } x +y&=10 \sqrt {x} \\
y \left (2\right ) &= 5 \\
\end{align*} |
✓ |
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| 7 |
\begin{align*}
2 y^{\prime } x +y&=10 \sqrt {x} \\
\end{align*} |
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| 8 |
\begin{align*}
y+3 y^{\prime } x&=12 x \\
\end{align*} |
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| 9 |
\begin{align*}
-y+y^{\prime } x&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
✓ |
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| 10 |
\begin{align*}
2 y^{\prime } x -3 y&=9 x^{3} \\
\end{align*} |
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| 11 |
\begin{align*}
y^{\prime } x +y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
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| 12 |
\begin{align*}
y^{\prime } x +3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
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| 13 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| 14 |
\begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
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| 15 |
\begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
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| 16 |
\begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
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| 17 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| 18 | \begin{align*}
y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 19 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
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| 20 |
\begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
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| 21 |
\begin{align*}
y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
✓ |
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| 22 |
\begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
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| 23 |
\begin{align*}
y^{\prime } x +\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
✓ |
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| 24 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| 25 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
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| 2 |
\begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime } x&=y+2 \sqrt {y x} \\
\end{align*} |
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| 4 |
\begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
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| 5 |
\begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
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| 6 |
\begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime } y^{2} x&=x^{3}+y^{3} \\
\end{align*} |
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| 8 |
\begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
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| 9 |
\begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
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| 10 |
\begin{align*}
y y^{\prime } x&=x^{2}+3 y^{2} \\
\end{align*} |
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| 11 |
\begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
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| 12 |
\begin{align*}
y y^{\prime } x&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \\
\end{align*} |
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| 13 |
\begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
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| 14 |
\begin{align*}
x +y y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
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| 15 |
\begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
✓ |
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| 16 |
\begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
✓ |
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| 17 |
\begin{align*}
y^{\prime }&=\left (4 x +y\right )^{2} \\
\end{align*} |
✓ |
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| 18 | \begin{align*}
\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 19 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
✓ |
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| 20 |
\begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
✓ |
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| 21 |
\begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
✓ |
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| 22 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
✓ |
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| 23 |
\begin{align*}
y^{\prime } x +6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
✓ |
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| 24 |
\begin{align*}
2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
✓ |
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| 25 |
\begin{align*}
y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
✓ |
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| 26 |
\begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
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| 27 |
\begin{align*}
3 y^{\prime } y^{2} x&=3 x^{4}+y^{3} \\
\end{align*} |
✓ |
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| 28 |
\begin{align*}
x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
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| 29 |
\begin{align*}
2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \\
\end{align*} |
✓ |
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| 30 |
\begin{align*}
\left ({\mathrm e}^{y}+x \right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\
\end{align*} |
✓ |
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| 31 |
\begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 32 |
\begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 33 |
\begin{align*}
3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 34 |
\begin{align*}
2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
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| 35 |
\begin{align*}
x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
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| 36 |
\begin{align*}
1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
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| 37 | \begin{align*}
\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
|
| 38 |
\begin{align*}
x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
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| 39 |
\begin{align*}
3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 40 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 41 |
\begin{align*}
\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 42 |
\begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x^{3}+3 y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
2 x y^{3}+{\mathrm e}^{x}+\left (3 y^{2} x^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 5 |
\begin{align*}
3 y+x^{4} y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 14 |
\begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
y^{\prime }&=x^{2}-2 y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\begin{align*}
{\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 18 | \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 19 |
\begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
y^{\prime } x +3 y&=\frac {3}{x^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (-1+x \right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\begin{align*}
y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\begin{align*}
{\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\begin{align*}
9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 25 |
\begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 26 |
\begin{align*}
9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 27 |
\begin{align*}
3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\begin{align*}
y^{\prime } x +y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 29 |
\begin{align*}
\left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 31(a) |
\begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 31 (b) |
\begin{align*}
y^{\prime }&=3 \left (y+7\right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 32 (b) |
\begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 33 (a) |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 34 (a) |
\begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 35 (a) |
\begin{align*}
y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 36 (a) |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
y^{\prime \prime }+25 y&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 13 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 7 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 33 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 34 | \begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 35 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 36 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 37 |
\begin{align*}
2 y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 38 |
\begin{align*}
4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 39 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 40 |
\begin{align*}
9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 41 |
\begin{align*}
6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 42 |
\begin{align*}
35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 52 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 53 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 54 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 55 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 56 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 21 |
\begin{align*}
y^{\prime \prime }+y&=3 x \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\begin{align*}
y^{\prime \prime }-4 y&=12 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 24 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 26(a.1) |
\begin{align*}
y^{\prime \prime }+2 y&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 26(a.2) |
\begin{align*}
y^{\prime \prime }+2 y&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 26(b) |
\begin{align*}
y^{\prime \prime }+2 y&=6 x +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\begin{align*}
9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 45 |
\begin{align*}
y^{\prime \prime }-2 i y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 46 |
\begin{align*}
y^{\prime \prime }-i y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 47 |
\begin{align*}
y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 52 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 53 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 15 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
3 x^{\prime \prime }+30 x^{\prime }+63 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\begin{align*}
x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\begin{align*}
2 x^{\prime \prime }+12 x^{\prime }+50 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 19 |
\begin{align*}
4 x^{\prime \prime }+20 x^{\prime }+169 x&=0 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
2 x^{\prime \prime }+16 x^{\prime }+40 x&=0 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
x^{\prime \prime }+10 x^{\prime }+125 x&=0 \\
x \left (0\right ) &= 6 \\
x^{\prime }\left (0\right ) &= 50 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=3 x +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
2 y^{\prime \prime }+4 y^{\prime }+7 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
y^{\prime \prime }-4 y&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\begin{align*}
y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 21 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\begin{align*}
y^{\prime \prime }+4 y&=3 x \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 25 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 26 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 31 |
\begin{align*}
y^{\prime \prime }+4 y&=2 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 32 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 33 | \begin{align*}
y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 34 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 35 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 44 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (3 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 45 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 46 |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 47 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 48 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 49 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 50 |
\begin{align*}
y^{\prime \prime }-4 y&=\sinh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 51 |
\begin{align*}
y^{\prime \prime }+4 y&=\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 52 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 53 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 54 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 55 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 56 |
\begin{align*}
y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 57 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 58 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 59 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 60 | \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 61 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 62 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\
x \left (0\right ) &= 375 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 90 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\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*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\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*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\
x \left (0\right ) &= 10 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\
x \left (0\right ) &= -30 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| problem 3 |
\begin{align*}
x^{\prime }\left (t \right )&=-3 y \left (t \right ) \\
y^{\prime }\left (t \right )&=3 x \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| problem 4 |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| problem 5 |
\begin{align*}
x^{\prime }\left (t \right )&=2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t} \\
y^{\prime }\left (t \right )&=5 x \left (t \right )-y \left (t \right )-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| problem 7 |
\begin{align*}
x^{\prime }\left (t \right )&=y \left (t \right )+z \left (t \right ) \\
y^{\prime }\left (t \right )&=x \left (t \right )+z \left (t \right ) \\
z^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| problem 11 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \\
x_{2}^{\prime }\left (t \right )&=2 x_{3} \left (t \right ) \\
x_{3}^{\prime }\left (t \right )&=3 x_{4} \left (t \right ) \\
x_{4}^{\prime }\left (t \right )&=4 x_{1} \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| problem 12 |
\begin{align*}
x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{3} \left (t \right )+1 \\
x_{2}^{\prime }\left (t \right )&=x_{3} \left (t \right )+x_{4} \left (t \right )+t \\
x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2} \\
x_{4}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|