| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 21701 |
\begin{align*}
y^{\prime }-\sin \left (x \right ) y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.289 |
|
| 21702 |
\begin{align*}
y^{\prime }&=-y^{3} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.290 |
|
| 21703 |
\begin{align*}
y^{\prime }&=y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.295 |
|
| 21704 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.295 |
|
| 21705 |
\begin{align*}
y^{\prime }&=\frac {x y}{x^{2}+1} \\
y \left (\sqrt {15}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.297 |
|
| 21706 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=1-\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.299 |
|
| 21707 |
\begin{align*}
3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.301 |
|
| 21708 |
\begin{align*}
y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.303 |
|
| 21709 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=4 x -6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.306 |
|
| 21710 |
\begin{align*}
y^{\prime }&=y^{p} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.311 |
|
| 21711 |
\begin{align*}
\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.312 |
|
| 21712 |
\begin{align*}
\left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.313 |
|
| 21713 |
\begin{align*}
2 y y^{\prime } x^{3}+a +3 y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.313 |
|
| 21714 |
\begin{align*}
3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.314 |
|
| 21715 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arcsin \left (x \right )^{n} y-a^{2}+a \lambda \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.319 |
|
| 21716 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.319 |
|
| 21717 |
\begin{align*}
y^{\prime } x&=y \left (2 y x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.322 |
|
| 21718 |
\begin{align*}
{y^{\prime }}^{2}&=a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.325 |
|
| 21719 |
\begin{align*}
x {y^{\prime }}^{2}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.327 |
|
| 21720 |
\begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.327 |
|
| 21721 |
\begin{align*}
\left (\sinh \left (\lambda x \right ) a +b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.328 |
|
| 21722 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.331 |
|
| 21723 |
\begin{align*}
b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.335 |
|
| 21724 |
\begin{align*}
\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (1+y^{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.336 |
|
| 21725 |
\begin{align*}
y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| 21726 |
\begin{align*}
y^{\prime } x +2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.344 |
|
| 21727 |
\begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.345 |
|
| 21728 |
\begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.347 |
|
| 21729 |
\begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.349 |
|
| 21730 |
\begin{align*}
x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.350 |
|
| 21731 |
\begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.352 |
|
| 21732 |
\begin{align*}
w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.352 |
|
| 21733 |
\begin{align*}
y^{\prime } x&=y-x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.356 |
|
| 21734 |
\begin{align*}
x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.356 |
|
| 21735 |
\begin{align*}
y^{\prime } x +2 y&=3 x -1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.357 |
|
| 21736 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=5 x \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| 21737 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.371 |
|
| 21738 |
\begin{align*}
\left (x +2 y+1\right ) y^{\prime }&=3+2 x +4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.376 |
|
| 21739 |
\begin{align*}
y^{\prime } x&=y f \left (x^{m} y^{n}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.377 |
|
| 21740 |
\begin{align*}
y-x \sqrt {x^{2}+y^{2}}+\left (x -y \sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.377 |
|
| 21741 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.378 |
|
| 21742 |
\begin{align*}
x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\
y \left (\infty \right ) &= 2 \pi \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.378 |
|
| 21743 |
\begin{align*}
x {y^{\prime }}^{2}&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.379 |
|
| 21744 |
\begin{align*}
y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.379 |
|
| 21745 |
\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*} |
✓ |
✓ |
✓ |
✓ |
8.380 |
|
| 21746 |
\begin{align*}
x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.381 |
|
| 21747 |
\begin{align*}
x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.385 |
|
| 21748 |
\begin{align*}
y^{\prime }&=t -y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.389 |
|
| 21749 |
\begin{align*}
y^{\prime }&=-\frac {2 y}{x}-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.391 |
|
| 21750 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.396 |
|
| 21751 |
\begin{align*}
y^{\prime }&=y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.398 |
|
| 21752 |
\begin{align*}
2 x +3 y+\left (y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.400 |
|
| 21753 |
\begin{align*}
x^{3} y^{\prime }&=\left (-1+y\right ) x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.408 |
|
| 21754 |
\begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.408 |
|
| 21755 |
\begin{align*}
6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.409 |
|
| 21756 |
\begin{align*}
x^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.413 |
|
| 21757 |
\begin{align*}
a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
8.415 |
|
| 21758 |
\begin{align*}
x y^{2} \left (y^{\prime } x +y\right )&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| 21759 |
\begin{align*}
y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.420 |
|
| 21760 |
\begin{align*}
-y+y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.420 |
|
| 21761 |
\begin{align*}
y^{\prime }&=\frac {F \left (\frac {1+x y^{2}}{x}\right )}{y x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.421 |
|
| 21762 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
8.422 |
|
| 21763 |
\begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.423 |
|
| 21764 |
\begin{align*}
-y+y^{\prime } x&=\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.424 |
|
| 21765 |
\begin{align*}
\left (t^{2}+1\right ) x^{\prime }&=-3 t x+6 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.426 |
|
| 21766 |
\begin{align*}
6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.428 |
|
| 21767 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.430 |
|
| 21768 |
\begin{align*}
2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.435 |
|
| 21769 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.437 |
|
| 21770 |
\begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.437 |
|
| 21771 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.438 |
|
| 21772 |
\begin{align*}
z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.441 |
|
| 21773 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.444 |
|
| 21774 |
\begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.450 |
|
| 21775 |
\begin{align*}
y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.451 |
|
| 21776 |
\begin{align*}
y^{\prime } x +2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.451 |
|
| 21777 |
\begin{align*}
y^{\prime }&=k \left (m^{4}-y^{4}\right ) \\
y \left (0\right ) &= \frac {m}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.457 |
|
| 21778 |
\begin{align*}
y^{\prime }-y x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.458 |
|
| 21779 |
\begin{align*}
y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.459 |
|
| 21780 |
\begin{align*}
y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.467 |
|
| 21781 |
\begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.471 |
|
| 21782 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+x^{m} b \right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.474 |
|
| 21783 |
\begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
8.475 |
|
| 21784 |
\begin{align*}
2 y y^{\prime } x&=a x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.481 |
|
| 21785 |
\begin{align*}
y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.482 |
|
| 21786 |
\begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.486 |
|
| 21787 |
\begin{align*}
y^{\prime }&=\left (x -y+5\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.489 |
|
| 21788 |
\begin{align*}
2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.492 |
|
| 21789 |
\begin{align*}
x^{2} y^{\prime }&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.494 |
|
| 21790 |
\begin{align*}
y^{\prime } x -\frac {y}{\ln \left (x \right )}&=0 \\
y \left ({\mathrm e}\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.494 |
|
| 21791 |
\begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.495 |
|
| 21792 |
\begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.495 |
|
| 21793 |
\begin{align*}
y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.497 |
|
| 21794 |
\begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.498 |
|
| 21795 |
\begin{align*}
x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.502 |
|
| 21796 |
\begin{align*}
y^{\prime } x&=\left (x +1\right ) y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.503 |
|
| 21797 |
\begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.509 |
|
| 21798 |
\begin{align*}
y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.514 |
|
| 21799 |
\begin{align*}
\left (a \ln \left (x \right )+b \right ) y^{\prime }&=y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.514 |
|
| 21800 |
\begin{align*}
y^{\prime } x&=y \left (2 y x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.515 |
|