| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15001 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.812 |
|
| 15002 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (a \left (2-n -m \right ) x^{2}-b \left (n +m \right ) x \right ) y^{\prime }+\left (a m \left (n -1\right ) x +b n \left (m +1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.812 |
|
| 15003 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| 15004 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| 15005 |
\begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| 15006 |
\begin{align*}
y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.812 |
|
| 15007 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| 15008 |
\begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| 15009 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| 15010 |
\begin{align*}
x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.814 |
|
| 15011 |
\begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.814 |
|
| 15012 |
\begin{align*}
y^{\prime }&=2 y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.815 |
|
| 15013 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.815 |
|
| 15014 |
\begin{align*}
y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| 15015 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| 15016 |
\begin{align*}
4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| 15017 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{2}&=y^{2} y^{\prime \prime } \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.817 |
|
| 15018 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| 15019 |
\begin{align*}
y^{\prime \prime }+a^{2} y-\cot \left (a x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| 15020 |
\begin{align*}
\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| 15021 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.817 |
|
| 15022 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.818 |
|
| 15023 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=A \cos \left (\omega x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.818 |
|
| 15024 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| 15025 |
\begin{align*}
y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| 15026 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| 15027 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.821 |
|
| 15028 |
\begin{align*}
y^{\prime }&=a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.821 |
|
| 15029 |
\begin{align*}
x^{\prime \prime }&=50 \sin \left (5 t \right ) \\
x \left (0\right ) &= 8 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| 15030 |
\begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| 15031 |
\begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| 15032 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.822 |
|
| 15033 |
\begin{align*}
2 y^{\prime } x&=y+2 \cos \left (x \right ) x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 15034 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 15035 |
\begin{align*}
x^{\prime }&=x-4 y+\cos \left (2 t \right ) \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 15036 |
\begin{align*}
y&=y^{\prime } x +a y^{\prime }+b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| 15037 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.824 |
|
| 15038 |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 15039 |
\begin{align*}
-\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 15040 |
\begin{align*}
\frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 15041 |
\begin{align*}
y^{\prime \prime }&=2 \csc \left (x \right )^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.825 |
|
| 15042 |
\begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 15043 |
\begin{align*}
t x^{\prime \prime }&=x \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.825 |
|
| 15044 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| 15045 |
\begin{align*}
y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| 15046 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| 15047 |
\begin{align*}
\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| 15048 |
\begin{align*}
x^{\prime }&=x+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| 15049 |
\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. |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| 15050 |
\begin{align*}
y^{\prime \prime }+4 y&=\sec \left (2 t \right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| 15051 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.830 |
|
| 15052 |
\begin{align*}
y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.830 |
|
| 15053 |
\begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.831 |
|
| 15054 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y&=4 x -8 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| 15055 |
\begin{align*}
y^{\prime \prime }+y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| 15056 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| 15057 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| 15058 |
\begin{align*}
x&=y y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.832 |
|
| 15059 |
\begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| 15060 |
\begin{align*}
y^{\prime }&=-\frac {y}{x -3} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| 15061 |
\begin{align*}
2 {y^{\prime }}^{2}-2 y y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.834 |
|
| 15062 |
\begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| 15063 |
\begin{align*}
y^{\prime }-2 t y&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| 15064 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.836 |
|
| 15065 |
\begin{align*}
y^{2} y^{\prime } x -y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.836 |
|
| 15066 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.837 |
|
| 15067 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.837 |
|
| 15068 |
\begin{align*}
y^{\prime }&=3 y+{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.837 |
|
| 15069 |
\begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| 15070 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| 15071 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| 15072 |
\begin{align*}
\left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| 15073 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| 15074 |
\begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1} \\
x_{3}^{\prime }&=-3 x_{4} \\
x_{4}^{\prime }&=3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| 15075 |
\begin{align*}
x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.839 |
|
| 15076 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.839 |
|
| 15077 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.839 |
|
| 15078 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.839 |
|
| 15079 |
\begin{align*}
y^{\prime \prime }&=a^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| 15080 |
\begin{align*}
w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.839 |
|
| 15081 |
\begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=x+3 y \\
z^{\prime }&=2 z+w+h \\
w^{\prime }&=z+2 w+h \\
h^{\prime }&=z+w+2 h \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| 15082 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.842 |
|
| 15083 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| 15084 |
\begin{align*}
x^{\prime }-x&=t x^{2} \\
x \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| 15085 |
\begin{align*}
x&=y-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| 15086 |
\begin{align*}
2 t y+\left (t^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.842 |
|
| 15087 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (a^{2} x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.843 |
|
| 15088 |
\begin{align*}
-y+y^{\prime }&=1+3 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| 15089 |
\begin{align*}
y^{\prime }&=y \left (1-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| 15090 |
\begin{align*}
2 y^{\prime }+2 \csc \left (x \right )^{2}&=y \csc \left (x \right ) \sec \left (x \right )-y^{2} \sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.845 |
|
| 15091 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| 15092 |
\begin{align*}
y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.847 |
|
| 15093 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \\
u \left (1\right ) &= 15 \\
u^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.847 |
|
| 15094 |
\begin{align*}
9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.848 |
|
| 15095 |
\begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.848 |
|
| 15096 |
\begin{align*}
2 \left (1-y\right )^{2} y-2 x \left (1-y\right ) y^{\prime }+2 x^{2} {y^{\prime }}^{2}+x^{2} \left (1-y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.849 |
|
| 15097 |
\begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.849 |
|
| 15098 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) {\mathrm e}^{-x}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.849 |
|
| 15099 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.850 |
|
| 15100 |
\begin{align*}
\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.850 |
|