| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17201 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| 17202 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| 17203 |
\begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| 17204 |
\begin{align*}
y^{\prime } x +2 y&=\frac {\sin \left (x \right )}{x} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.195 |
|
| 17205 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.195 |
|
| 17206 |
\begin{align*}
y^{\prime }-y^{2}-y x -x +1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.195 |
|
| 17207 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.195 |
|
| 17208 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 17209 |
\begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.197 |
|
| 17210 |
\begin{align*}
16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 17211 |
\begin{align*}
x^{\prime }+2 x&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 17212 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| 17213 |
\begin{align*}
x^{\prime }&=2 t x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| 17214 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| 17215 |
\begin{align*}
y^{\prime \prime }+2 n \cot \left (x n \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.199 |
|
| 17216 |
\begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 17217 |
\begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 17218 |
\begin{align*}
y^{\prime }-3 y&=6 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 17219 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 17220 |
\begin{align*}
y^{\prime } x&=x^{m}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 17221 |
\begin{align*}
x +y^{2}+B \left (x \right ) y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 17222 |
\begin{align*}
y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.201 |
|
| 17223 |
\begin{align*}
4 x {y^{\prime }}^{2}+2 y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.202 |
|
| 17224 |
\begin{align*}
16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.202 |
|
| 17225 |
\begin{align*}
y^{\prime } x +\left (2+5 x \right ) y&=\frac {20}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.202 |
|
| 17226 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.202 |
|
| 17227 |
\begin{align*}
y^{\prime \prime }+36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| 17228 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| 17229 |
\begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\
y \left (\frac {1}{4}\right ) &= 0 \\
y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| 17230 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| 17231 |
\begin{align*}
y&={y^{\prime }}^{2}-y^{\prime } x +x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.204 |
|
| 17232 |
\begin{align*}
2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| 17233 |
\begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.205 |
|
| 17234 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.205 |
|
| 17235 |
\begin{align*}
{\mathrm e}^{x}-\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.206 |
|
| 17236 |
\begin{align*}
y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.207 |
|
| 17237 |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=t^{3}+2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.207 |
|
| 17238 |
\begin{align*}
x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| 17239 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.208 |
|
| 17240 |
\begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 17241 |
\begin{align*}
y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 17242 |
\begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.210 |
|
| 17243 |
\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*} |
✓ |
✓ |
✓ |
✓ |
2.210 |
|
| 17244 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| 17245 |
\begin{align*}
y^{\prime } x -2 y&=-x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| 17246 |
\begin{align*}
y^{\prime }-y x&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| 17247 |
\begin{align*}
y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| 17248 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| 17249 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.211 |
|
| 17250 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.212 |
|
| 17251 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| 17252 |
\begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.214 |
|
| 17253 |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.214 |
|
| 17254 |
\begin{align*}
-y+y^{\prime } x&=2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.215 |
|
| 17255 |
\begin{align*}
y^{\prime \prime }-x^{2} y-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.216 |
|
| 17256 |
\begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 17257 |
\begin{align*}
y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.217 |
|
| 17258 |
\begin{align*}
{\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-{\mathrm e}^{y} y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 17259 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 17260 |
\begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| 17261 |
\begin{align*}
r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| 17262 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| 17263 |
\begin{align*}
{y^{\prime }}^{3} x -y {y^{\prime }}^{2}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.220 |
|
| 17264 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.220 |
|
| 17265 |
\begin{align*}
3 x^{2}-2 y x +\left (4 y^{3}-x^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.220 |
|
| 17266 |
\begin{align*}
y&=\tan \left (x \right ) y^{\prime }-{y^{\prime }}^{2} \sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.220 |
|
| 17267 |
\begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.221 |
|
| 17268 |
\begin{align*}
y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.221 |
|
| 17269 |
\begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.221 |
|
| 17270 |
\begin{align*}
\left (6+3 y x -4 y^{3}\right ) x +\left (x^{3}-6 y^{2} x^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.221 |
|
| 17271 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&={\mathrm e}^{\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.222 |
|
| 17272 |
\begin{align*}
t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.223 |
|
| 17273 |
\begin{align*}
y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| 17274 |
\begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| 17275 |
\begin{align*}
y^{\prime }&={\mathrm e}^{y+t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| 17276 |
\begin{align*}
y^{\prime \prime }-2 x^{2} y-x^{4}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.224 |
|
| 17277 |
\begin{align*}
y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.224 |
|
| 17278 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.226 |
|
| 17279 |
\begin{align*}
2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 17280 |
\begin{align*}
t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 17281 |
\begin{align*}
2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.226 |
|
| 17282 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y&=x^{m} \ln \left (x \right )^{k} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 17283 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 17284 |
\begin{align*}
y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| 17285 |
\begin{align*}
\frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.228 |
|
| 17286 |
\begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.228 |
|
| 17287 |
\begin{align*}
x y \left (1+y^{2}\right )+\left (y^{2} x^{2}-2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.228 |
|
| 17288 |
\begin{align*}
\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.229 |
|
| 17289 |
\begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| 17290 |
\begin{align*}
4 {y^{\prime }}^{3} x -6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.230 |
|
| 17291 |
\begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 17292 |
\begin{align*}
x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\
z \left (1\right ) &= 0 \\
z^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 17293 |
\begin{align*}
x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| 17294 |
\begin{align*}
y^{\prime } x +x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| 17295 |
\begin{align*}
y^{\prime }&=y \ln \left (y+2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| 17296 |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right ) y^{{1}/{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.234 |
|
| 17297 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.234 |
|
| 17298 |
\begin{align*}
3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.234 |
|
| 17299 |
\begin{align*}
y^{\prime }&=\frac {a x +b}{y^{n}+d} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| 17300 |
\begin{align*}
t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.234 |
|