| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x y^{\prime }&=x^{2}+2 x -3 \\
\end{align*} |
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| 2 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime }&=1+y^{2} \\
\end{align*} |
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| 3 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{3 x} \\
\end{align*} |
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| 4 |
\begin{align*}
x y^{\prime }-y&=x^{2} \\
\end{align*} |
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| 5 |
\begin{align*}
x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\
\end{align*} |
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| 6 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=0 \\
\end{align*} |
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| 7 |
\begin{align*}
\left (x y^{2}+x^{3}\right ) y^{\prime }&=2 y^{3} \\
\end{align*} |
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| 8 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\
\end{align*} |
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| 9 |
\begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\
\end{align*} |
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| 10 |
\begin{align*}
x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\
\end{align*} |
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| 11 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=y^{3} \\
\end{align*} |
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| 12 |
\begin{align*}
x y^{\prime }+3 y&=x^{2} y^{2} \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x \left (-3+y\right ) y^{\prime }&=4 y \\
\end{align*} |
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| 2 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\
y \left (1\right ) &= 2 \\
\end{align*} |
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| 3 |
\begin{align*}
x^{3}+\left (y+1\right )^{2} y^{\prime }&=0 \\
\end{align*} |
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| 4 |
\begin{align*}
\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= \frac {\pi }{4} \\
\end{align*} |
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| 5 |
\begin{align*}
x^{2} \left (y+1\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
\left (-x +2 y\right ) y^{\prime }&=2 x +y \\
\end{align*} |
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| 7 |
\begin{align*}
y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
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| 8 |
\begin{align*}
x^{3}+y^{3}&=3 x y^{2} y^{\prime } \\
\end{align*} |
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| 9 |
\begin{align*}
y-3 x +\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 10 |
\begin{align*}
\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=y^{3}+3 x^{2} y \\
\end{align*} |
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| 11 |
\begin{align*}
x y^{\prime }-y&=x^{3}+3 x^{2}-2 x \\
\end{align*} |
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| 12 |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sin \left (x \right ) \\
\end{align*} |
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| 13 |
\begin{align*}
x y^{\prime }-y&=x^{3} \cos \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
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| 14 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
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| 15 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=5 \,{\mathrm e}^{\cos \left (x \right )} \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*} |
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| 16 |
\begin{align*}
\left (3 x +3 y-4\right ) y^{\prime }&=-x -y \\
\end{align*} |
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| 17 |
\begin{align*}
x -x y^{2}&=\left (x +x^{2} y\right ) y^{\prime } \\
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| 18 | \begin{align*}
x -y-1+\left (4 y+x -1\right ) y^{\prime }&=0 \\
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| 19 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
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| 20 |
\begin{align*}
\left (y x +1\right ) y+x \left (1+y x +x^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 21 |
\begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
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| 22 |
\begin{align*}
y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\
\end{align*} |
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| 23 |
\begin{align*}
2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\
\end{align*} |
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| 24 |
\begin{align*}
y^{\prime }-2 y \tan \left (x \right )&=y^{2} \tan \left (x \right )^{2} \\
\end{align*} |
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| 25 |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=y^{3} \sec \left (x \right )^{4} \\
\end{align*} |
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| 26 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
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| 27 |
\begin{align*}
x y y^{\prime }-\left (x +1\right ) \sqrt {-1+y}&=0 \\
\end{align*} |
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| 29 |
\begin{align*}
y^{\prime }-y \cot \left (x \right )&=y^{2} \sec \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -1 \\
\end{align*} |
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| 30 |
\begin{align*}
y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
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| 31 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
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| 32 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}+2 y x} \\
\end{align*} |
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| 33 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (y+1\right ) \\
\end{align*} |
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| 34 |
\begin{align*}
x y^{\prime }+2 y&=3 x -1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
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| 35 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}-x y y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
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| 36 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 37 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
\end{align*} |
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| 38 | \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 39 |
\begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
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| 40 |
\begin{align*}
y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
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| 41 |
\begin{align*}
\left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \\
\end{align*} |
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| 42 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
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| 43 |
\begin{align*}
y^{\prime }+x +x y^{2}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
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| 44 |
\begin{align*}
y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \\
\end{align*} |
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| 45 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
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| 46 |
\begin{align*}
x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\
\end{align*} |
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| 47 |
\begin{align*}
\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\
r \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
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| 48 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 49 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=8 \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime \prime }-4 y&=10 \,{\mathrm e}^{3 x} \\
\end{align*} |
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| 3 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime \prime }+25 y&=5 x^{2}+x \\
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| 5 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \\
\end{align*} |
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| 6 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
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| 7 |
\begin{align*}
3 y^{\prime \prime }-2 y^{\prime }-y&=2 x -3 \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }-4 y&={\mathrm e}^{3 x} \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=54 x +18 \\
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| 3 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=100 \sin \left (4 x \right ) \\
\end{align*} |
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| 4 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \sinh \left (x \right ) \\
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| 5 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 \cosh \left (2 x \right ) \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \cos \left (x \right )^{2} \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=x +{\mathrm e}^{2 x} \\
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| 9 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+3 y&=x^{2}-1 \\
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| 10 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (x \right ) \\
\end{align*} |
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| 12 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
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| 13 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=6 \sin \left (t \right ) \\
\end{align*} |
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| 14 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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| 15 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=3 \sin \left (x \right ) \\
y \left (0\right ) &= -{\frac {9}{10}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{10}} \\
\end{align*} |
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| 16 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+10 y&=50 x \\
\end{align*} |
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| 17 |
\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*} |
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| 18 |
\begin{align*}
y^{\prime \prime }&=3 \sin \left (x \right )-4 y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
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| 19 | \begin{align*}
\frac {x^{\prime \prime }}{2}&=-48 x \\
x \left (0\right ) &= {\frac {1}{6}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 20 |
\begin{align*}
x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\
x \left (0\right ) &= {\frac {1}{10}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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