| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18501 |
\begin{align*}
y^{\prime }&=y^{4} \cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| 18502 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.321 |
|
| 18503 |
\begin{align*}
x^{\prime }&=\lambda x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| 18504 |
\begin{align*}
x y^{2}+y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| 18505 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| 18506 |
\begin{align*}
x y^{\prime }-\frac {y}{\ln \left (x \right )}&=0 \\
y \left ({\mathrm e}\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.324 |
|
| 18507 |
\begin{align*}
x^{\prime }&=x \left (4+x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.325 |
|
| 18508 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.326 |
|
| 18509 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.326 |
|
| 18510 |
\begin{align*}
3 x^{2} {\mathrm e}^{x^{3}}+{\mathrm e}^{2 y}+\left (2 x \,{\mathrm e}^{2 y}-3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.326 |
|
| 18511 |
\begin{align*}
y \left (x +y\right )+\left (y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.326 |
|
| 18512 |
\begin{align*}
v \left (2 u v^{2}-3\right )+\left (3 u^{2} v^{2}-3 u +4 v\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.327 |
|
| 18513 |
\begin{align*}
3 y+x^{3} y^{4}+3 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| 18514 |
\begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| 18515 |
\begin{align*}
N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| 18516 |
\begin{align*}
\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| 18517 |
\begin{align*}
3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| 18518 |
\begin{align*}
t^{2} y^{\prime }+2 y t&=1 \\
y \left (2\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.329 |
|
| 18519 |
\begin{align*}
y^{\prime }&=\left (t^{2}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.330 |
|
| 18520 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.330 |
|
| 18521 |
\begin{align*}
\ln \left (y\right ) y-2 y x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.330 |
|
| 18522 |
\begin{align*}
2 x -1-\frac {y}{x^{2}}-\left (2 y-\frac {1}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.330 |
|
| 18523 |
\begin{align*}
y^{\prime }&=\frac {1+\cos \left (x \right )}{2-\sin \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.331 |
|
| 18524 |
\begin{align*}
2-2 x +3 y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.331 |
|
| 18525 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.332 |
|
| 18526 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| 18527 |
\begin{align*}
y^{\prime }&=1+\left (-x +y\right )^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| 18528 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| 18529 |
\begin{align*}
y^{\prime \prime }+\left (\cos \left (x \right )^{2} a +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.333 |
|
| 18530 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=x^{2}+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.333 |
|
| 18531 |
\begin{align*}
y^{3} y^{\prime \prime }+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.335 |
|
| 18532 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.336 |
|
| 18533 |
\begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.336 |
|
| 18534 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.338 |
|
| 18535 |
\begin{align*}
x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.338 |
|
| 18536 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
3.338 |
|
| 18537 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.339 |
|
| 18538 |
\begin{align*}
2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.339 |
|
| 18539 |
\begin{align*}
y^{\prime }&=1+a \left (x -y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.340 |
|
| 18540 |
\begin{align*}
1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.341 |
|
| 18541 |
\begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.341 |
|
| 18542 |
\begin{align*}
y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.341 |
|
| 18543 |
\begin{align*}
-x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| 18544 |
\begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| 18545 |
\begin{align*}
2 y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
y \left (3\right ) &= 1 \\
y^{\prime }\left (3\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.346 |
|
| 18546 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.347 |
|
| 18547 |
\begin{align*}
x&=x^{\prime } t +\frac {1}{x^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.349 |
|
| 18548 |
\begin{align*}
y^{\prime }&=\frac {y}{3 x -y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.349 |
|
| 18549 |
\begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.350 |
|
| 18550 |
\begin{align*}
\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.350 |
|
| 18551 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.351 |
|
| 18552 |
\begin{align*}
9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| 18553 |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=8 \sin \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| 18554 |
\begin{align*}
1&=\left (x +y^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.353 |
|
| 18555 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
3.353 |
|
| 18556 |
\begin{align*}
x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.353 |
|
| 18557 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.355 |
|
| 18558 |
\begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} t^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.355 |
|
| 18559 |
\begin{align*}
\left (6+3 y x -4 y^{3}\right ) x +\left (x^{3}-6 x^{2} y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.355 |
|
| 18560 |
\begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.357 |
|
| 18561 |
\begin{align*}
y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x}&=0 \\
y \left (1\right ) &= 0 \\
y \left ({\mathrm e}^{\pi }\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.357 |
|
| 18562 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.358 |
|
| 18563 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.359 |
|
| 18564 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \\
y \left (\pi \right ) &= \pi \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| 18565 |
\begin{align*}
x y^{\prime }-4 y&=x^{2} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| 18566 |
\begin{align*}
2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.361 |
|
| 18567 |
\begin{align*}
\left (x +1\right ) y^{\prime }-x^{2} y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| 18568 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| 18569 |
\begin{align*}
1+{\mathrm e}^{y t} \left (1+y t \right )+\left (1+{\mathrm e}^{y t} t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.363 |
|
| 18570 |
\begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.364 |
|
| 18571 |
\begin{align*}
y y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.364 |
|
| 18572 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.365 |
|
| 18573 |
\begin{align*}
a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.366 |
|
| 18574 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.368 |
|
| 18575 |
\begin{align*}
x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.368 |
|
| 18576 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.369 |
|
| 18577 |
\begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.369 |
|
| 18578 |
\begin{align*}
y^{\prime }&=-\frac {-x^{2}+2 x^{3} y-F \left (\left (y x -1\right ) x \right )}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.369 |
|
| 18579 |
\begin{align*}
x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.370 |
|
| 18580 |
\begin{align*}
2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.370 |
|
| 18581 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.371 |
|
| 18582 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{-2+n}+b m \left (m -1\right ) x^{m -2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.371 |
|
| 18583 |
\begin{align*}
3 y^{\prime }+y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.371 |
|
| 18584 |
\begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.372 |
|
| 18585 |
\begin{align*}
b y+2 \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.373 |
|
| 18586 |
\begin{align*}
y^{\prime }-4 y&=2 x y^{2} \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| 18587 |
\begin{align*}
y^{\prime } \sin \left (y\right )&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| 18588 |
\begin{align*}
y^{\prime }&=\frac {1}{x -y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| 18589 |
\begin{align*}
y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.374 |
|
| 18590 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.375 |
|
| 18591 |
\begin{align*}
4 a y^{\prime \prime }+b y^{\prime }+\frac {c y}{4}&=f \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.375 |
|
| 18592 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.376 |
|
| 18593 |
\begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.376 |
|
| 18594 |
\begin{align*}
x y^{\prime }+\frac {\left (2 x +1\right ) y}{x +1}&=x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.377 |
|
| 18595 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.378 |
|
| 18596 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.378 |
|
| 18597 |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.380 |
|
| 18598 |
\begin{align*}
\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.380 |
|
| 18599 |
\begin{align*}
x y^{\prime }+x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.381 |
|
| 18600 |
\begin{align*}
y^{\prime }&=\frac {F \left (-\frac {2 y \ln \left (x \right )-1}{y}\right ) y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.381 |
|