| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15301 |
\begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| 15302 |
\begin{align*}
y^{\prime }&=y \left (t y^{3}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| 15303 |
\begin{align*}
4 y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| 15304 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| 15305 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.946 |
|
| 15306 |
\begin{align*}
y^{\prime \prime \prime }+y&={\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.946 |
|
| 15307 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
1.946 |
|
| 15308 |
\begin{align*}
2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.948 |
|
| 15309 |
\begin{align*}
y^{\prime } x +2 y&=\frac {2}{x^{2}}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.949 |
|
| 15310 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.949 |
|
| 15311 |
\begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.950 |
|
| 15312 |
\begin{align*}
\left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| 15313 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b \right ) x y^{\prime }+\left (3 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.951 |
|
| 15314 |
\begin{align*}
u^{\prime \prime }+2 u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.952 |
|
| 15315 |
\begin{align*}
y^{\prime }-2 y x&=1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.952 |
|
| 15316 |
\begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.952 |
|
| 15317 |
\begin{align*}
x^{2} y^{\prime }+3 y x&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| 15318 |
\begin{align*}
x {y^{\prime }}^{2}+y y^{\prime }&=3 y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| 15319 |
\begin{align*}
y^{\prime }&=\left (t -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| 15320 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.954 |
|
| 15321 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.954 |
|
| 15322 |
\begin{align*}
\left (y^{2} a^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.954 |
|
| 15323 |
\begin{align*}
5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.954 |
|
| 15324 |
\begin{align*}
y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.955 |
|
| 15325 |
\begin{align*}
y x +x +2 y+1+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.956 |
|
| 15326 |
\begin{align*}
y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.956 |
|
| 15327 |
\begin{align*}
y^{\prime \prime }&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| 15328 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.957 |
|
| 15329 |
\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*} |
✓ |
✓ |
✓ |
✗ |
1.957 |
|
| 15330 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.958 |
|
| 15331 |
\begin{align*}
x^{\prime \prime }+\lambda x-x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.958 |
|
| 15332 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.959 |
|
| 15333 |
\begin{align*}
y^{\prime \prime }&=\frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.959 |
|
| 15334 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.959 |
|
| 15335 |
\begin{align*}
y-1-y x +y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| 15336 |
\begin{align*}
x^{2} y^{\prime }-y&=x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| 15337 |
\begin{align*}
y^{\prime }+a y-b \sin \left (c x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| 15338 |
\begin{align*}
2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.960 |
|
| 15339 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| 15340 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.961 |
|
| 15341 |
\begin{align*}
x +y^{2}+B \left (x \right ) y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.961 |
|
| 15342 |
\begin{align*}
x^{\prime }&=x-x^{2} \\
x \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.962 |
|
| 15343 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.962 |
|
| 15344 |
\begin{align*}
y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.963 |
|
| 15345 |
\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*} |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| 15346 |
\begin{align*}
y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| 15347 |
\begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.966 |
|
| 15348 |
\begin{align*}
y {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.966 |
|
| 15349 |
\begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.967 |
|
| 15350 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3} \\
x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\
x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\
x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.968 |
|
| 15351 |
\begin{align*}
y^{\prime }&=2 y-4 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.968 |
|
| 15352 |
\begin{align*}
y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.968 |
|
| 15353 |
\begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
1.968 |
|
| 15354 |
\begin{align*}
y^{\prime }&=b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| 15355 |
\begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| 15356 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.971 |
|
| 15357 |
\begin{align*}
\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| 15358 |
\begin{align*}
1+y-\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| 15359 |
\begin{align*}
y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| 15360 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| 15361 |
\begin{align*}
\left (x -4\right ) y^{\prime \prime }+4 y^{\prime }-\frac {4 y}{x -4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| 15362 |
\begin{align*}
y^{\prime }&=\left (1-y^{2}\right ) \left (4-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.971 |
|
| 15363 |
\begin{align*}
y^{\prime }-\frac {y}{3}&=3 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.972 |
|
| 15364 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= \sqrt {2} \\
y^{\prime }\left (1\right ) &= 3 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.973 |
|
| 15365 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.973 |
|
| 15366 |
\begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.973 |
|
| 15367 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.973 |
|
| 15368 |
\begin{align*}
y^{\prime }&=\frac {2 y-x +5}{2 x -y-4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| 15369 |
\begin{align*}
s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| 15370 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.976 |
|
| 15371 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.977 |
|
| 15372 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-\ln \left (x \right ) x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.977 |
|
| 15373 |
\begin{align*}
2 t y+y^{\prime }&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.978 |
|
| 15374 |
\begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }&=\left (1-3 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.979 |
|
| 15375 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.979 |
|
| 15376 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.979 |
|
| 15377 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.981 |
|
| 15378 |
\begin{align*}
y^{\prime \prime }&=\operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.982 |
|
| 15379 |
\begin{align*}
4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.982 |
|
| 15380 |
\begin{align*}
y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| 15381 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| 15382 |
\begin{align*}
x^{\prime }&=x^{3}-x \\
x \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| 15383 |
\begin{align*}
y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.985 |
|
| 15384 |
\begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.986 |
|
| 15385 |
\begin{align*}
1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.986 |
|
| 15386 |
\begin{align*}
y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.986 |
|
| 15387 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{t}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.986 |
|
| 15388 |
\begin{align*}
y^{\prime }-y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.986 |
|
| 15389 |
\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*} |
✓ |
✓ |
✗ |
✗ |
1.987 |
|
| 15390 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.988 |
|
| 15391 |
\begin{align*}
y^{\prime } x +a x y^{2}+2 y+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.988 |
|
| 15392 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=8 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.988 |
|
| 15393 |
\begin{align*}
y^{\prime }&={\mathrm e}^{a x}+a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.989 |
|
| 15394 |
\begin{align*}
y^{\prime } x&=1-x +2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.989 |
|
| 15395 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| 15396 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| 15397 |
\begin{align*}
\left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| 15398 |
\begin{align*}
y^{\prime \prime }&=\frac {a}{y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| 15399 |
\begin{align*}
y+3 y^{\prime }&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.992 |
|
| 15400 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.992 |
|