| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16101 |
\begin{align*}
y^{\prime }&=3 x -y \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 16102 |
\begin{align*}
x^{\prime }-x&=\frac {t}{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 16103 |
\begin{align*}
x^{2}+y+\left (x +{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.198 |
|
| 16104 |
\begin{align*}
y^{\prime }&=2 y+\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| 16105 |
\begin{align*}
y^{\prime }&=5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.199 |
|
| 16106 |
\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*} |
✓ |
✓ |
✓ |
✗ |
2.200 |
|
| 16107 |
\begin{align*}
x y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 16108 |
\begin{align*}
y+y^{\prime }&=\delta \left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 16109 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.201 |
|
| 16110 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 16111 |
\begin{align*}
y^{\prime \prime }-a^{2} y&=f \left (t \right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 16112 |
\begin{align*}
y^{\prime }&=F \left (\frac {y}{x +a}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.202 |
|
| 16113 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a \,x^{3} b -a \,x^{2}+b^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.203 |
|
| 16114 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| 16115 |
\begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| 16116 |
\begin{align*}
y^{\prime }+y \ln \left (y\right ) \tan \left (x \right )&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| 16117 |
\begin{align*}
y^{\prime }&=-y+3 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| 16118 |
\begin{align*}
y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.205 |
|
| 16119 |
\begin{align*}
x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| 16120 |
\begin{align*}
x^{\prime }&=\frac {y}{10} \\
y^{\prime }&=\frac {z}{5} \\
z^{\prime }&=\frac {2 x}{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| 16121 |
\begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| 16122 |
\begin{align*}
y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| 16123 |
\begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| 16124 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| 16125 |
\begin{align*}
x y^{\prime \prime }&={y^{\prime }}^{2} x +y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| 16126 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| 16127 |
\begin{align*}
s^{\prime \prime }+s^{\prime }&=t +{\mathrm e}^{-t} \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| 16128 |
\begin{align*}
3 x y^{2}-12 x^{2} y y^{\prime }+4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}+8 \left (-x^{3}+1\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.209 |
|
| 16129 |
\begin{align*}
y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.209 |
|
| 16130 |
\begin{align*}
y^{\prime }+y&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.209 |
|
| 16131 |
\begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 16132 |
\begin{align*}
y^{\prime }&=t +\frac {2 y}{t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 16133 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\
x_{3}^{\prime }&=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\
x_{4}^{\prime }&=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 16134 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 16135 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 16136 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 16137 |
\begin{align*}
2 y x -2 y+1+x \left (x -1\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.212 |
|
| 16138 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=1-3 \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| 16139 |
\begin{align*}
4 y+y^{\prime \prime }&=\cos \left (x \right ) \cos \left (2 x \right ) \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| 16140 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=5 \sqrt {x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.213 |
|
| 16141 |
\begin{align*}
4 y+3 x y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| 16142 |
\begin{align*}
y^{\prime }-y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.215 |
|
| 16143 |
\begin{align*}
{\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0 \\
x \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.216 |
|
| 16144 |
\begin{align*}
y^{\prime }+y&=2 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 16145 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 16146 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 16147 |
\begin{align*}
x y^{\prime }+y&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 16148 |
\begin{align*}
3 {y^{\prime }}^{3}-x y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 16149 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.218 |
|
| 16150 |
\begin{align*}
x^{\prime }&=2 x+5 y \\
y^{\prime }&=-2 x+\cos \left (3 t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| 16151 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| 16152 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.220 |
|
| 16153 |
\begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| 16154 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| 16155 |
\begin{align*}
2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.222 |
|
| 16156 |
\begin{align*}
y^{\prime }+5 y&={\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| 16157 |
\begin{align*}
y^{\prime }-3 y&=\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| 16158 |
\begin{align*}
10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=-1+3 x^{2}+2 x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.224 |
|
| 16159 |
\begin{align*}
x y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 16160 |
\begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 16161 |
\begin{align*}
2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 16162 |
\begin{align*}
x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.224 |
|
| 16163 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.224 |
|
| 16164 |
\begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 16165 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.225 |
|
| 16166 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 16167 |
\begin{align*}
2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| 16168 |
\begin{align*}
\left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| 16169 |
\begin{align*}
a x y+2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 16170 |
\begin{align*}
y^{\prime }+y&=\left (x +1\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 16171 |
\begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| 16172 |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 16173 |
\begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 16174 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 16175 |
\begin{align*}
x y^{\prime \prime }+3 y^{\prime }-y&=x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| 16176 |
\begin{align*}
y^{\prime }&=\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| 16177 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.228 |
|
| 16178 |
\begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= -{\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.228 |
|
| 16179 |
\begin{align*}
y^{\prime \prime }-9 y&=36 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.229 |
|
| 16180 |
\begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.229 |
|
| 16181 |
\begin{align*}
x y^{\prime }+2 y&=\frac {\sin \left (x \right )}{x} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 16182 |
\begin{align*}
{y^{\prime }}^{2} x +x y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 16183 |
\begin{align*}
x^{\prime \prime }+16 x&=0 \\
x \left (0\right ) &= -2 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 16184 |
\begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16185 |
\begin{align*}
-\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16186 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16187 |
\begin{align*}
y^{\prime }-2 y x&=-1 \\
y \left (0\right ) &= \frac {\sqrt {\pi }}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16188 |
\begin{align*}
\left (1+z^{\prime }\right ) {\mathrm e}^{-z}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16189 |
\begin{align*}
a {y^{\prime }}^{2}+b y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16190 |
\begin{align*}
y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 16191 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.231 |
|
| 16192 |
\begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| 16193 |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.232 |
|
| 16194 |
\begin{align*}
6 x^{5} y+\left (y^{4} \ln \left (y\right )-3 x^{6}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| 16195 |
\begin{align*}
x y^{\prime }+3 y&=\frac {2}{x \left (x^{2}+1\right )} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| 16196 |
\begin{align*}
t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| 16197 |
\begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| 16198 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 4 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.234 |
|
| 16199 |
\begin{align*}
x y^{\prime }-y&=x^{2} \\
y \left (2\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| 16200 |
\begin{align*}
x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.235 |
|