| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1.1 |
\begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
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| 1.2 |
\begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 1.3 |
\begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
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| 1.4 |
\begin{align*}
1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\
\end{align*} |
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| 1.5 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 1.6 |
\begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
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| 3.1 |
\begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
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| 3.2 |
\begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
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| 3.3 |
\begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
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| 3.4 |
\begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 3.5 |
\begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
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| 4.1 |
\begin{align*}
2 x -y+1+\left (-1+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 4.2 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
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| 6.1 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\
\end{align*} |
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| 6.2 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
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| 6.3 |
\begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
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| 6.4 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
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| 6.5 | \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
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| 10.1 |
\begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\
\end{align*} |
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| 10.2 |
\begin{align*}
3 z^{2} z^{\prime }-a z^{3}&=x +1 \\
\end{align*} |
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| 10.3 |
\begin{align*}
z^{\prime }+2 x z&=2 a \,x^{3} z^{3} \\
\end{align*} |
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| 10.4 |
\begin{align*}
z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\
\end{align*} |
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| 10.5 |
\begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
\frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 4 |
\begin{align*}
x +y y^{\prime }+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
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| 5 |
\begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
{\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
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| 7 |
\begin{align*}
n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
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| 8.1 |
\begin{align*}
\frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2 |
\begin{align*}
2 y x +\left (y^{2}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 4 |
\begin{align*}
\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
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| 5.1 |
\begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
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| 5.2 |
\begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
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| 5.3 |
\begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 5.4 |
\begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 5.4 |
\begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y+\left (x \cos \left (\frac {y}{x}\right )-\sin \left (\frac {y}{x}\right ) y\right ) x y^{\prime }&=0 \\
\end{align*} |
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| 7.1 |
\begin{align*}
\left (x^{2} y^{2}+y x \right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
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| 7.1 |
\begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1.1 |
\begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
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| 1.2 |
\begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
y+\left (-x +2 y\right ) y^{\prime }&=0 \\
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x y^{\prime }-a y+y^{2}&=x^{-2 a} \\
\end{align*} |
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| 2 |
\begin{align*}
x y^{\prime }-a y+y^{2}&=x^{-\frac {2 a}{3}} \\
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| 3 |
\begin{align*}
u^{\prime }+u^{2}&=\frac {c}{x^{{4}/{3}}} \\
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| 4 |
\begin{align*}
u^{\prime }+b u^{2}&=\frac {c}{x^{4}} \\
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| 5 |
\begin{align*}
u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\
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| 12 |
\begin{align*}
\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}&=-1 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\
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| 3 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1-x}{x} \\
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| 4 |
\begin{align*}
{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\
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| 5 |
\begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
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| 6 |
\begin{align*}
x&=a y^{\prime }+b {y^{\prime }}^{2} \\
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| 7 |
\begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
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| 8 |
\begin{align*}
x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
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| 9 |
\begin{align*}
y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \\
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| 10 |
\begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
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| 11 |
\begin{align*}
1+{y^{\prime }}^{2}&=\frac {\left (x +a \right )^{2}}{2 a x +x^{2}} \\
\end{align*} |
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| 12 |
\begin{align*}
y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\
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| 13 |
\begin{align*}
y&=x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
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| 14 |
\begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
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| 15 |
\begin{align*}
y&=x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}} \\
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| 16 |
\begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
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| 17 |
\begin{align*}
y y^{\prime }+x&=a \sqrt {1+{y^{\prime }}^{2}} \\
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| 18 | \begin{align*}
y y^{\prime }&=x +y^{2}-y^{2} {y^{\prime }}^{2} \\
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| 19 |
\begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
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| 20 |
\begin{align*}
y-2 x y^{\prime }&={y^{\prime }}^{2} x \\
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| 21 |
\begin{align*}
\frac {y-x y^{\prime }}{y^{\prime }+y^{2}}&=\frac {y-x y^{\prime }}{1+x^{2} y^{\prime }} \\
\end{align*} |
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