| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 11001 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.549 |
|
| 11002 |
\begin{align*}
y^{\prime }&=\frac {a y+b}{d +c y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 11003 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 11004 |
\begin{align*}
4 x^{2} y^{\prime \prime }+y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 11005 |
\begin{align*}
\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 11006 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| 11007 |
\begin{align*}
{y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.550 |
|
| 11008 |
\begin{align*}
y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.551 |
|
| 11009 |
\begin{align*}
x^{\prime \prime }+x {x^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.552 |
|
| 11010 |
\begin{align*}
x^{2} y^{\prime \prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 11011 |
\begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| 11012 |
\begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 11013 |
\begin{align*}
t \left (1+t \right ) y^{\prime }&=2+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| 11014 |
\begin{align*}
t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 11015 |
\begin{align*}
x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| 11016 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| 11017 |
\begin{align*}
x^{\prime }&=2 x-5 y+\sin \left (t \right ) \\
y^{\prime }&=x-2 y+\tan \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 11018 |
\begin{align*}
-2 y+y^{\prime }&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 11019 |
\begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 11020 |
\begin{align*}
y^{\prime }&=1-\cot \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 11021 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| 11022 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 11023 |
\begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 11024 |
\begin{align*}
y^{\prime } x +\left (x +1\right ) y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 11025 |
\begin{align*}
x^{\prime }+x \cot \left (y \right )&=\sec \left (y \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 11026 |
\begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| 11027 |
\begin{align*}
y^{\prime }&=x \sec \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 11028 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| 11029 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.559 |
|
| 11030 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 11031 |
\begin{align*}
y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y&=\sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 11032 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=1+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 11033 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| 11034 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| 11035 |
\begin{align*}
x^{3} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.562 |
|
| 11036 |
\begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 11037 |
\begin{align*}
\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 11038 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.563 |
|
| 11039 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| 11040 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.564 |
|
| 11041 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| 11042 |
\begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 11043 |
\begin{align*}
y^{\prime }&=y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.566 |
|
| 11044 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| 11045 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.567 |
|
| 11046 |
\begin{align*}
\left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.567 |
|
| 11047 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| 11048 |
\begin{align*}
y^{\prime \prime }+y&=x \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.570 |
|
| 11049 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| 11050 |
\begin{align*}
u^{\prime }&=-a \left (u-100 t \right ) \\
u \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| 11051 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| 11052 |
\begin{align*}
2 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| 11053 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| 11054 |
\begin{align*}
x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\
y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\
z^{\prime }&=-x+6 y+z+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| 11055 |
\begin{align*}
t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| 11056 |
\begin{align*}
y^{\prime }+y^{2}-3 y+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| 11057 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\
x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| 11058 |
\begin{align*}
x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\
x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.574 |
|
| 11059 |
\begin{align*}
y^{\prime }&=\frac {x +y^{4}-2 y^{2} x^{2}+x^{4}}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.574 |
|
| 11060 |
\begin{align*}
y^{\prime } x -1+y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.574 |
|
| 11061 |
\begin{align*}
y^{\prime \prime }-2 r y^{\prime }+\left (r^{2}-\frac {\alpha ^{2}}{4}\right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.574 |
|
| 11062 |
\begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 11063 |
\begin{align*}
y^{\prime }&=y+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| 11064 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.576 |
|
| 11065 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| 11066 |
\begin{align*}
y^{\prime }&=\frac {1}{2 t -2 y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| 11067 |
\begin{align*}
R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\
R \left (1\right ) &= 3 \ln \left (2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.577 |
|
| 11068 |
\begin{align*}
4 y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| 11069 |
\begin{align*}
y^{\prime \prime \prime }-5 y^{\prime } x&={\mathrm e}^{x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| 11070 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| 11071 |
\begin{align*}
3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.579 |
|
| 11072 |
\begin{align*}
x {y^{\prime }}^{2}+x y y^{\prime \prime }&=3 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.579 |
|
| 11073 |
\begin{align*}
\cos \left (x \right ) u^{\prime \prime }+\sin \left (x \right ) u^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) u&=0 \\
u \left (\frac {\pi }{4}\right ) &= 2 \\
u^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} Series expansion around \(x=\frac {\pi }{4}\). |
✓ |
✓ |
✓ |
✗ |
1.579 |
|
| 11074 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=9 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| 11075 |
\begin{align*}
r^{3} r^{\prime }&=\sqrt {a^{8}-r^{8}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| 11076 |
\begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.580 |
|
| 11077 |
\begin{align*}
y^{\prime }&=\ln \left (1+x^{2}+y^{2}\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.581 |
|
| 11078 |
\begin{align*}
10 x_{1}^{\prime }&=-x_{1}+x_{3} \\
10 x_{2}^{\prime }&=x_{1}-x_{2} \\
10 x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| 11079 |
\begin{align*}
y^{\prime }&=\left (1+t \right ) \left (1+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| 11080 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| 11081 |
\begin{align*}
\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| 11082 |
\begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.583 |
|
| 11083 |
\begin{align*}
y^{\prime \prime }+\frac {\left ({\mathrm e}^{x}+1\right ) y}{1-{\mathrm e}^{x}}&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.584 |
|
| 11084 |
\begin{align*}
y^{\prime \prime }&=\left (1+y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.584 |
|
| 11085 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.585 |
|
| 11086 |
\begin{align*}
x^{\prime }+2 x&=t^{2}+4 t +7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.585 |
|
| 11087 |
\begin{align*}
r^{\prime }&={\mathrm e}^{t}-3 r \\
r \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.585 |
|
| 11088 |
\begin{align*}
y^{\prime } x +y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.585 |
|
| 11089 |
\begin{align*}
y^{\prime }&=a +b x +c y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| 11090 |
\begin{align*}
{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| 11091 |
\begin{align*}
y^{\prime }&=y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.586 |
|
| 11092 |
\begin{align*}
{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| 11093 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.587 |
|
| 11094 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| 11095 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.589 |
|
| 11096 |
\begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 9 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| 11097 |
\begin{align*}
y^{\prime \prime }+2 z y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| 11098 |
\begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.590 |
|
| 11099 |
\begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.590 |
|
| 11100 |
\begin{align*}
L i^{\prime }+R i&=E \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.590 |
|