| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18201 |
\begin{align*}
y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| 18202 |
\begin{align*}
2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| 18203 |
\begin{align*}
y^{\prime }&=\left (\frac {1+y^{2}}{x^{4}+1}\right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.185 |
|
| 18204 |
\begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| 18205 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )-y \sec \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| 18206 |
\begin{align*}
x y^{\prime }&=a \,x^{3} \left (-y x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| 18207 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| 18208 |
\begin{align*}
\left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 x y^{4}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| 18209 |
\begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| 18210 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| 18211 |
\begin{align*}
y x^{\prime }+2 x&=5 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| 18212 |
\begin{align*}
x^{\prime }&=2 t^{3} x-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| 18213 |
\begin{align*}
y^{\prime }-2 y&=\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| 18214 |
\begin{align*}
y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.188 |
|
| 18215 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.189 |
|
| 18216 |
\begin{align*}
x^{\prime }+x \tanh \left (t \right )&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.190 |
|
| 18217 |
\begin{align*}
x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u&=0 \\
u \left (1\right ) &= -1 \\
u^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.190 |
|
| 18218 |
\begin{align*}
\left (x +{\mathrm e}^{y}\right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| 18219 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.191 |
|
| 18220 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| 18221 |
\begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| 18222 |
\begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.193 |
|
| 18223 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=f \left (x \right ) \left (1-y\right ) y y^{\prime }+\left (-2 y+1\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.194 |
|
| 18224 |
\begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.194 |
|
| 18225 |
\begin{align*}
4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.195 |
|
| 18226 |
\begin{align*}
x^{2} y^{\prime }+2 y x -x +1&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| 18227 |
\begin{align*}
x y^{\prime \prime }+3 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| 18228 |
\begin{align*}
t y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| 18229 |
\begin{align*}
x y^{\prime }+a y+b \,x^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.197 |
|
| 18230 |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+\left (n -1\right ) n \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.197 |
|
| 18231 |
\begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| 18232 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| 18233 |
\begin{align*}
v-\left ({\mathrm e}^{v}+2 u v-2 u \right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.198 |
|
| 18234 |
\begin{align*}
y^{\prime }&=2 t \left (1+y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.199 |
|
| 18235 |
\begin{align*}
1+y^{2}&=x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.199 |
|
| 18236 |
\begin{align*}
y^{\prime }&=\sin \left (2 x \right )+y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| 18237 |
\begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| 18238 |
\begin{align*}
x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| 18239 |
\begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| 18240 |
\begin{align*}
y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| 18241 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| 18242 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \\
y \left (1\right ) &= 1+\cos \left (2\right ) \\
y^{\prime }\left (1\right ) &= 4-2 \sin \left (2\right ) \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| 18243 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.201 |
|
| 18244 |
\begin{align*}
{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| 18245 |
\begin{align*}
{\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| 18246 |
\begin{align*}
y-\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.202 |
|
| 18247 |
\begin{align*}
\left (x \cos \left (y\right )-{\mathrm e}^{-\sin \left (y\right )}\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.202 |
|
| 18248 |
\begin{align*}
\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=\left (2 x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.203 |
|
| 18249 |
\begin{align*}
2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.204 |
|
| 18250 |
\begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| 18251 |
\begin{align*}
y^{\prime }+y \ln \left (x \right )&=x^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| 18252 |
\begin{align*}
x y^{\prime }&=y x +y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| 18253 |
\begin{align*}
y^{\prime }+\left (b x +a \right ) y&=f \left (x \right ) \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| 18254 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.204 |
|
| 18255 |
\begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.205 |
|
| 18256 |
\begin{align*}
y^{\prime }-\frac {2 t y}{t^{2}+1}&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.206 |
|
| 18257 |
\begin{align*}
2 y \ln \left (x \right ) \ln \left (y\right )+x \left (\ln \left (x \right )^{2}+\ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.206 |
|
| 18258 |
\begin{align*}
x y^{\prime }&=y+x^{2} \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| 18259 |
\begin{align*}
y+y^{\prime }&=5 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| 18260 |
\begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.207 |
|
| 18261 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| 18262 |
\begin{align*}
\tan \left (y\right )&=\left (3 x +4\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| 18263 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\left (2 t^{2}+t +1\right ) \delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| 18264 |
\begin{align*}
y^{\prime }&=\frac {1}{x \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| 18265 |
\begin{align*}
y^{\prime }&=\frac {y}{x +1}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| 18266 |
\begin{align*}
y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.209 |
|
| 18267 |
\begin{align*}
y^{\prime }&=a y^{\frac {a -1}{a}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.210 |
|
| 18268 |
\begin{align*}
y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.210 |
|
| 18269 |
\begin{align*}
x y^{\prime }&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.210 |
|
| 18270 |
\begin{align*}
y^{\prime }&=\sin \left (x \right )+2 y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.211 |
|
| 18271 |
\begin{align*}
\left (-y^{\prime }+x y^{\prime \prime }\right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.211 |
|
| 18272 |
\begin{align*}
y^{\prime }&=\frac {x}{-y+1+y^{4}+2 x^{2} y^{2}+x^{4}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.211 |
|
| 18273 |
\begin{align*}
y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.211 |
|
| 18274 |
\begin{align*}
3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.212 |
|
| 18275 |
\begin{align*}
x^{3}+x y^{2}+y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.212 |
|
| 18276 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y&={\mathrm e}^{x} \cos \left (x \right )+x^{2}+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.213 |
|
| 18277 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| 18278 |
\begin{align*}
x^{\prime \prime }-4 x&=1-\operatorname {Heaviside}\left (t -1\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| 18279 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| 18280 |
\begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| 18281 |
\begin{align*}
y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.215 |
|
| 18282 |
\begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| 18283 |
\begin{align*}
y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.217 |
|
| 18284 |
\begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| 18285 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.219 |
|
| 18286 |
\begin{align*}
y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| 18287 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.220 |
|
| 18288 |
\begin{align*}
2 y^{\prime }+y^{2}+\frac {1}{x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| 18289 |
\begin{align*}
y&=\left ({\mathrm e}^{y}+2 y x -2 x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.221 |
|
| 18290 |
\begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.221 |
|
| 18291 |
\begin{align*}
y^{\prime \prime }+k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.222 |
|
| 18292 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.222 |
|
| 18293 |
\begin{align*}
y^{\prime }&=\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.223 |
|
| 18294 |
\begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.223 |
|
| 18295 |
\begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{3}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.223 |
|
| 18296 |
\begin{align*}
\left (x -2\right ) y^{\prime }&=y+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.224 |
|
| 18297 |
\begin{align*}
y^{\prime }+y^{2}+4 y x +4 x^{2}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| 18298 |
\begin{align*}
\left (a^{2} x^{2}+2\right ) y-2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| 18299 |
\begin{align*}
y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| 18300 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.226 |
|