| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23401 |
\begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.694 |
|
| 23402 |
\begin{align*}
x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.695 |
|
| 23403 |
\begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.696 |
|
| 23404 |
\begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.700 |
|
| 23405 |
\begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.701 |
|
| 23406 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }&=f \left (y^{\prime }\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.704 |
|
| 23407 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {1-y^{2}}{-x^{2}+1}} \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.704 |
|
| 23408 |
\begin{align*}
x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.711 |
|
| 23409 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.715 |
|
| 23410 |
\begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.717 |
|
| 23411 |
\begin{align*}
2 \left (x -y^{2}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.721 |
|
| 23412 |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x^{2} \ln \left (x \right )^{2}+2 x^{2} \ln \left (y\right ) \ln \left (x \right )+x^{2} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.724 |
|
| 23413 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (b \,x^{2}+a \left (x^{4}+1\right )\right ) y}{x^{4}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.724 |
|
| 23414 |
\begin{align*}
m y^{\prime \prime }+k y&=0 \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.726 |
|
| 23415 |
\begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.727 |
|
| 23416 |
\begin{align*}
2 y t +y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.727 |
|
| 23417 |
\begin{align*}
2 y y^{\prime \prime }&=4 y^{2}+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.734 |
|
| 23418 |
\begin{align*}
\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.734 |
|
| 23419 |
\begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.735 |
|
| 23420 |
\begin{align*}
z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.735 |
|
| 23421 |
\begin{align*}
{\mathrm e}^{t} y^{\prime }&=y^{3}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.739 |
|
| 23422 |
\begin{align*}
y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.741 |
|
| 23423 |
\begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.743 |
|
| 23424 |
\begin{align*}
x +y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.743 |
|
| 23425 |
\begin{align*}
x^{2} \left (y^{\prime }-1\right )&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.744 |
|
| 23426 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=\left (-x -y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.748 |
|
| 23427 |
\begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.753 |
|
| 23428 |
\begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.759 |
|
| 23429 |
\begin{align*}
-y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.760 |
|
| 23430 |
\begin{align*}
\left (x +y-1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| 23431 |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+x^{2} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
9.768 |
|
| 23432 |
\begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.775 |
|
| 23433 |
\begin{align*}
x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y&=\sin \left (x \right ) \cos \left (x \right )-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.776 |
|
| 23434 |
\begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.776 |
|
| 23435 |
\begin{align*}
y^{\prime \prime }&=f \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.778 |
|
| 23436 |
\begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.779 |
|
| 23437 |
\begin{align*}
y^{\prime }&=\sin \left (t -y\right )+\sin \left (t +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.782 |
|
| 23438 |
\begin{align*}
y^{\prime }&=-\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.784 |
|
| 23439 |
\begin{align*}
x y^{\prime }&=y^{2}-y \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.799 |
|
| 23440 |
\begin{align*}
y^{\prime \prime }&=\left (-x +a \right ) {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.800 |
|
| 23441 |
\begin{align*}
\left (\sin \left (x \right )+y\right ) y^{\prime }+\cos \left (x \right ) y-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.803 |
|
| 23442 |
\begin{align*}
L q^{\prime \prime }+R q^{\prime }+\frac {q}{c}&=E_{0} \sin \left (\omega t \right ) \\
q \left (0\right ) &= 0 \\
q^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.811 |
|
| 23443 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.813 |
|
| 23444 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.815 |
|
| 23445 |
\begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.816 |
|
| 23446 |
\begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.817 |
|
| 23447 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+3 y&=\left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
9.823 |
|
| 23448 |
\begin{align*}
y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.824 |
|
| 23449 |
\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*} |
✓ |
✓ |
✓ |
✓ |
9.835 |
|
| 23450 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.837 |
|
| 23451 |
\begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.838 |
|
| 23452 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.839 |
|
| 23453 |
\begin{align*}
a \left (x y^{\prime }+2 y\right )&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.839 |
|
| 23454 |
\begin{align*}
x +2 y+3+\left (2 x +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.842 |
|
| 23455 |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {1+4 x^{2} y}\, x^{4}}{2 x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.844 |
|
| 23456 |
\begin{align*}
3 t y^{\prime }&=\cos \left (t \right ) y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.849 |
|
| 23457 |
\begin{align*}
x^{\prime }&=x^{2}-t^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.850 |
|
| 23458 |
\begin{align*}
y^{\prime }&=\frac {\left (t +1\right )^{2}}{\left (1+y\right )^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.852 |
|
| 23459 |
\begin{align*}
y^{\prime }&=x \left (y-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.852 |
|
| 23460 |
\begin{align*}
2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.853 |
|
| 23461 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.856 |
|
| 23462 |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.863 |
|
| 23463 |
\begin{align*}
5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.868 |
|
| 23464 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.872 |
|
| 23465 |
\begin{align*}
y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.880 |
|
| 23466 |
\begin{align*}
y^{\prime \prime }&=3 \sqrt {y} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.885 |
|
| 23467 |
\begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.888 |
|
| 23468 |
\begin{align*}
\left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.889 |
|
| 23469 |
\begin{align*}
y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\
y \left (\frac {1}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.896 |
|
| 23470 |
\begin{align*}
y^{\prime }&=\frac {\cot \left (y\right )}{t} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.899 |
|
| 23471 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| 23472 |
\begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| 23473 |
\begin{align*}
1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.913 |
|
| 23474 |
\begin{align*}
2 n y-2 x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.914 |
|
| 23475 |
\begin{align*}
y^{\prime }&=x y^{2}-2 y+4-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.914 |
|
| 23476 |
\begin{align*}
{y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.915 |
|
| 23477 |
\begin{align*}
6 y x +2 y^{2}-5+\left (3 x^{2}+4 y x -6\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.924 |
|
| 23478 |
\begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
9.928 |
|
| 23479 |
\begin{align*}
2 a \,x^{3} y-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.928 |
|
| 23480 |
\begin{align*}
\left (a \,x^{n}+b \right ) y^{\prime }&=b y^{2}+a \,x^{-2+n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.942 |
|
| 23481 |
\begin{align*}
4 \left (x -1\right )^{2} y^{\prime }-3 \left (y+3\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.948 |
|
| 23482 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.950 |
|
| 23483 |
\begin{align*}
y^{\prime }&=\frac {1+2 x^{5} \sqrt {1+4 x^{2} y}}{2 x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.953 |
|
| 23484 |
\begin{align*}
{\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.953 |
|
| 23485 |
\begin{align*}
3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.958 |
|
| 23486 |
\begin{align*}
y^{\prime }&=\frac {y+1}{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.964 |
|
| 23487 |
\begin{align*}
y^{\prime }&=y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.965 |
|
| 23488 |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.967 |
|
| 23489 |
\begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.970 |
|
| 23490 |
\begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.974 |
|
| 23491 |
\begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.981 |
|
| 23492 |
\begin{align*}
y y^{\prime }&=2 x \sec \left (3 y\right ) \\
y \left (\frac {2}{3}\right ) &= \frac {\pi }{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
9.985 |
|
| 23493 |
\begin{align*}
3 x y^{2} y^{\prime }&=2 x -y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.994 |
|
| 23494 |
\begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.997 |
|
| 23495 |
\begin{align*}
\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.000 |
|
| 23496 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=\frac {1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.000 |
|
| 23497 |
\begin{align*}
y-x \sqrt {x^{2}+y^{2}}+\left (x -y \sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.000 |
|
| 23498 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{{5}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.001 |
|
| 23499 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
10.001 |
|
| 23500 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.003 |
|