| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2 |
\begin{align*}
x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 y^{\prime } x +4 y&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime }+c y&=a \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y&=0 \\
\end{align*} |
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| 5 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right )&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\
\end{align*} |
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| 16 (a) |
\begin{align*}
v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\
\end{align*} |
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| 16 (b) |
\begin{align*}
v^{\prime }+u^{2} v&=\sin \left (u \right ) \\
\end{align*} |
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| 17 (a) |
\begin{align*}
\sqrt {y^{\prime }+y}&=\left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \\
\end{align*} |
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| 18 |
\begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 4 (a) |
\begin{align*}
\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
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| 4 (b) |
\begin{align*}
y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}}&=0 \\
\end{align*} |
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| 4 (c) |
\begin{align*}
y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
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| 5 |
\begin{align*}
x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )} \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{2}&=x \left (-x +y\right ) y^{\prime } \\
\end{align*} |
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| 2 |
\begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\
\end{align*} |
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| 4 |
\begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right ) y^{\prime }+\sec \left (y\right )^{2} \tan \left (x \right )&=0 \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime } y+x&=m y \\
\end{align*} |
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| 6 |
\begin{align*}
\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} |
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| 8 |
\begin{align*}
\left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime }&=\frac {T}{t \sqrt {t^{2}-T^{2}}}-t \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }+y x&=x \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {\sin \left (x \right )}{y^{3}} \\
\end{align*} |
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| 4 |
\begin{align*}
p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\
\end{align*} |
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| 5 |
\begin{align*}
\left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }+y \cos \left (x \right )&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
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| 7 |
\begin{align*}
y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2 |
\begin{align*}
{y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime }&={\mathrm e}^{z -y^{\prime }} \\
\end{align*} |
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| 5 |
\begin{align*}
\sqrt {t^{2}+T}&=T^{\prime } \\
\end{align*} |
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| 7 |
\begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )&=1 \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
\theta ^{\prime \prime }&=-p^{2} \theta \\
\end{align*} |
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| 2 (eq 39) |
\begin{align*}
\sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\
\end{align*} |
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| 3 (eq 41) |
\begin{align*}
y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \\
\end{align*} |
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| 4 (eq 50) |
\begin{align*}
\phi ^{\prime \prime }&=\frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \\
\end{align*} |
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| 8 (eq 68) |
\begin{align*}
y^{\prime }&=x \left (a y^{2}+b \right ) \\
\end{align*} |
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| 8 (eq 69) |
\begin{align*}
n^{\prime }&=\left (n^{2}+1\right ) x \\
\end{align*} |
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| 9 (a) |
\begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 v \\
\end{align*} |
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| 9 (b) |
\begin{align*}
\sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\
\end{align*} |
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| 9 (c) |
\begin{align*}
\sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\
\end{align*} |
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| 9 (d) |
\begin{align*}
\frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\
\end{align*} |
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| 9 (e) |
\begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
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| 10 (a) |
\begin{align*}
v^{\prime }+2 u v&=2 u \\
\end{align*} |
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| 10 (b) |
\begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
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| 10 (c) |
\begin{align*}
u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 (eq 100) |
\begin{align*}
\theta ^{\prime \prime }-p^{2} \theta &=0 \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime \prime }+12 y&=7 y^{\prime } \\
\end{align*} |
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| 4 |
\begin{align*}
r^{\prime \prime }-a^{2} r&=0 \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime \prime \prime \prime }-a^{4} y&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-y&=\sin \left (t \right ) \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime \prime }+3 y&=\sin \left (x \right )+\frac {\sin \left (3 x \right )}{3} \\
\end{align*} |
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| 10 |
\begin{align*}
5 x^{\prime }+x&=\sin \left (3 t \right ) \\
\end{align*} |
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| 11 |
\begin{align*}
x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
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| 14 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x&=17 x^{6} \\
\end{align*} |
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| 15 |
\begin{align*}
t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x&=\cos \left (3 \ln \left (t \right )\right ) \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\
\end{align*} |
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| 8 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
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