| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17001 |
\begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.602 |
|
| 17002 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3}+1 \\
x_{2}^{\prime }&=x_{3}+x_{4}+t \\
x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\
x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.604 |
|
| 17003 |
\begin{align*}
\left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.604 |
|
| 17004 |
\begin{align*}
3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.605 |
|
| 17005 |
\begin{align*}
t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.605 |
|
| 17006 |
\begin{align*}
x^{4} \left (y^{\prime }-y^{2}\right )&=a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.605 |
|
| 17007 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.605 |
|
| 17008 |
\begin{align*}
y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| 17009 |
\begin{align*}
y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.606 |
|
| 17010 |
\begin{align*}
x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| 17011 |
\begin{align*}
y^{\prime \prime }&=-m^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| 17012 |
\begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| 17013 |
\begin{align*}
4 x^{2} y^{2} {y^{\prime }}^{2}&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| 17014 |
\begin{align*}
y^{\prime \prime }&=2 \csc \left (x \right )^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.608 |
|
| 17015 |
\begin{align*}
-y+y^{\prime }&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| 17016 |
\begin{align*}
x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.608 |
|
| 17017 |
\begin{align*}
y^{\prime }+2 y&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| 17018 |
\begin{align*}
2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| 17019 |
\begin{align*}
x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| 17020 |
\begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.609 |
|
| 17021 |
\begin{align*}
a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.609 |
|
| 17022 |
\begin{align*}
x y^{\prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.610 |
|
| 17023 |
\begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.610 |
|
| 17024 |
\begin{align*}
\left (-1+y\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.610 |
|
| 17025 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| 17026 |
\begin{align*}
r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| 17027 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\arcsin \left (\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| 17028 |
\begin{align*}
\left (x +1\right ) \left (y y^{\prime }-1\right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| 17029 |
\begin{align*}
x^{2} y^{\prime }-y&=x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.612 |
|
| 17030 |
\begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.612 |
|
| 17031 |
\begin{align*}
y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| 17032 |
\begin{align*}
3 y^{2} y^{\prime }+y^{3}&=x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| 17033 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| 17034 |
\begin{align*}
y x&=\left (y^{3}+x^{2} y+x^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| 17035 |
\begin{align*}
\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.616 |
|
| 17036 |
\begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.618 |
|
| 17037 |
\begin{align*}
-2 y+2 x y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.619 |
|
| 17038 |
\begin{align*}
L i^{\prime }+R i&=E \sin \left (2 t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| 17039 |
\begin{align*}
t^{2} x^{\prime \prime }-7 x^{\prime } t +16 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| 17040 |
\begin{align*}
y^{\prime }+3 y&=3 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| 17041 |
\begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| 17042 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=2-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.620 |
|
| 17043 |
\begin{align*}
y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.620 |
|
| 17044 |
\begin{align*}
2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\
y \left (4\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.621 |
|
| 17045 |
\begin{align*}
-\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.622 |
|
| 17046 |
\begin{align*}
y^{\prime }&=2 y+\cos \left (4 t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.622 |
|
| 17047 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| 17048 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| 17049 |
\begin{align*}
x y^{\prime }-y&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| 17050 |
\begin{align*}
y+y^{\prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| 17051 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=-\frac {16 \ln \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| 17052 |
\begin{align*}
3 x^{2} y^{2}-4 y+\left (3 y^{2}-4 x +2 x^{3} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.625 |
|
| 17053 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.626 |
|
| 17054 |
\begin{align*}
y^{\prime }&=x +5 y \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.627 |
|
| 17055 |
\begin{align*}
a^{2} x^{a -1} y+\left (1-2 a \right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.628 |
|
| 17056 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.629 |
|
| 17057 |
\begin{align*}
x y^{\prime \prime }+x y^{\prime }-y&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.629 |
|
| 17058 |
\begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.630 |
|
| 17059 |
\begin{align*}
y^{\prime }&=\frac {y \left (x +y\right )}{x \left (y^{3}+x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.630 |
|
| 17060 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.631 |
|
| 17061 |
\begin{align*}
x \left (x +1\right ) \left (y^{\prime }-1\right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.631 |
|
| 17062 |
\begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.632 |
|
| 17063 |
\begin{align*}
y y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.633 |
|
| 17064 |
\begin{align*}
y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.633 |
|
| 17065 |
\begin{align*}
x y^{\prime }-y-x^{2} \sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| 17066 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| 17067 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| 17068 |
\begin{align*}
x \,{\mathrm e}^{-y^{2}}+y y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| 17069 |
\begin{align*}
y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.634 |
|
| 17070 |
\begin{align*}
y^{\prime }&=y-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| 17071 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=2 x^{2}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| 17072 |
\begin{align*}
\cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| 17073 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| 17074 |
\begin{align*}
-y+t y^{\prime }&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| 17075 |
\begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| 17076 |
\begin{align*}
x \left (x -1\right ) y^{\prime }+2 y x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| 17077 |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| 17078 |
\begin{align*}
y^{\prime }-y \cot \left (x \right )&=2 x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| 17079 |
\begin{align*}
x y^{\prime }&=x^{4}+4 y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| 17080 |
\begin{align*}
\theta ^{\prime \prime }&=-p^{2} \theta \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| 17081 |
\begin{align*}
y^{\prime }&=\frac {t}{y-t^{2} y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.639 |
|
| 17082 |
\begin{align*}
{x^{\prime }}^{2}-x t +x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.639 |
|
| 17083 |
\begin{align*}
3 \left (-1+y\right ) x +y+2+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.640 |
|
| 17084 |
\begin{align*}
\left (4-y^{2}\right ) y^{\prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| 17085 |
\begin{align*}
2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.642 |
|
| 17086 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| 17087 |
\begin{align*}
y^{\prime \prime }&=-\frac {A y}{\left (a \,x^{2}+b x +c \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.643 |
|
| 17088 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.643 |
|
| 17089 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=\left (x +2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.643 |
|
| 17090 |
\begin{align*}
s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.643 |
|
| 17091 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| 17092 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+9 y&=20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.645 |
|
| 17093 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| 17094 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 17095 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 17096 |
\begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y \left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 17097 |
\begin{align*}
3 y+y^{\prime }&=-10 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| 17098 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| 17099 |
\begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| 17100 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.649 |
|