| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18701 |
\begin{align*}
\theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.426 |
|
| 18702 |
\begin{align*}
y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.428 |
|
| 18703 |
\begin{align*}
y^{\prime }+2 y&=5 \delta \left (t -1\right ) \\
y \left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.428 |
|
| 18704 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.430 |
|
| 18705 |
\begin{align*}
x^{n} y^{\prime }&=a +b \,x^{n -1} y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.431 |
|
| 18706 |
\begin{align*}
y^{\prime }+y&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.432 |
|
| 18707 |
\begin{align*}
y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.432 |
|
| 18708 |
\begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.432 |
|
| 18709 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.434 |
|
| 18710 |
\begin{align*}
i^{\prime }+5 i&=10 \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.434 |
|
| 18711 |
\begin{align*}
y^{\prime } x&=a x +b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.438 |
|
| 18712 |
\begin{align*}
\cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.440 |
|
| 18713 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.441 |
|
| 18714 |
\begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.441 |
|
| 18715 |
\begin{align*}
y^{\prime \prime }+2 z y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.442 |
|
| 18716 |
\begin{align*}
y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.444 |
|
| 18717 |
\begin{align*}
x +y y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.445 |
|
| 18718 |
\begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.447 |
|
| 18719 |
\begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.451 |
|
| 18720 |
\begin{align*}
y^{\prime } \left (1+\sin \left (x \right )\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.451 |
|
| 18721 |
\begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.451 |
|
| 18722 |
\begin{align*}
x^{\prime }&=t x-t^{3} \\
x \left (0\right ) &= a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.457 |
|
| 18723 |
\begin{align*}
\left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.458 |
|
| 18724 |
\begin{align*}
4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\
x \left (1\right ) &= 2 \\
x^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.459 |
|
| 18725 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 12 \\
y^{\prime }\left (0\right ) &= 7 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
y^{\prime \prime \prime }\left (0\right ) &= -9 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.461 |
|
| 18726 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.463 |
|
| 18727 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= {\mathrm e}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.467 |
|
| 18728 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.467 |
|
| 18729 |
\begin{align*}
y^{\prime }&=\frac {\left (y-a \ln \left (y\right ) x +x^{2}\right ) y}{\left (-y \ln \left (y\right )-y \ln \left (x \right )-y+a x \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.469 |
|
| 18730 |
\begin{align*}
y^{\prime \prime } x +\left (x +a +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.469 |
|
| 18731 |
\begin{align*}
{y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.469 |
|
| 18732 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.469 |
|
| 18733 |
\begin{align*}
x^{\prime \prime }+\pi ^{2} x&=\pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.470 |
|
| 18734 |
\begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.470 |
|
| 18735 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.471 |
|
| 18736 |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\
y \left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.473 |
|
| 18737 |
\begin{align*}
x^{\prime }-x+2 y^{\prime }&=0 \\
4 x^{\prime }+3 y^{\prime }+y&=-6 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.474 |
|
| 18738 |
\begin{align*}
y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.474 |
|
| 18739 |
\begin{align*}
y^{\prime \prime }&=y^{3}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.476 |
|
| 18740 |
\begin{align*}
x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\
y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\
z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.477 |
|
| 18741 |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {10 \pi }{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.477 |
|
| 18742 |
\begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.477 |
|
| 18743 |
\begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.484 |
|
| 18744 |
\begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.487 |
|
| 18745 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (2 x \right )+\sin \left (2 x \right )+2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.489 |
|
| 18746 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.490 |
|
| 18747 |
\begin{align*}
y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.491 |
|
| 18748 |
\begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.492 |
|
| 18749 |
\begin{align*}
{\mathrm e}^{x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.492 |
|
| 18750 |
\begin{align*}
y^{\prime }+y x&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.493 |
|
| 18751 |
\begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.495 |
|
| 18752 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (-1+x \right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (-1+x \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.496 |
|
| 18753 |
\begin{align*}
y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.497 |
|
| 18754 |
\begin{align*}
y^{\prime }-4 y&=-8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.497 |
|
| 18755 |
\begin{align*}
x^{n} y^{\prime }&=x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.500 |
|
| 18756 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.501 |
|
| 18757 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.504 |
|
| 18758 |
\begin{align*}
2 x^{2} y y^{\prime }&=x^{2} \left (2 x +1\right )-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.506 |
|
| 18759 |
\begin{align*}
{y^{\prime }}^{2}&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.507 |
|
| 18760 |
\begin{align*}
y \ln \left (y\right )-2 y x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.508 |
|
| 18761 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.510 |
|
| 18762 |
\begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.512 |
|
| 18763 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.516 |
|
| 18764 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-y}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.516 |
|
| 18765 |
\begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.519 |
|
| 18766 |
\begin{align*}
\csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.521 |
|
| 18767 |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.522 |
|
| 18768 |
\begin{align*}
y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.523 |
|
| 18769 |
\begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.524 |
|
| 18770 |
\begin{align*}
y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.525 |
|
| 18771 |
\begin{align*}
\left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.526 |
|
| 18772 |
\begin{align*}
y^{\prime }&=\frac {x +y+y^{2}-2 x y \ln \left (x \right )+\ln \left (x \right )^{2} x^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.527 |
|
| 18773 |
\begin{align*}
y \sin \left (y x \right )+x y^{2} \cos \left (y x \right )+\left (x \sin \left (y x \right )+x y^{2} \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.529 |
|
| 18774 |
\begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.530 |
|
| 18775 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.531 |
|
| 18776 |
\begin{align*}
y^{\prime } x +y&={\mathrm e}^{x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.532 |
|
| 18777 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.532 |
|
| 18778 |
\begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.533 |
|
| 18779 |
\begin{align*}
\left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.533 |
|
| 18780 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.535 |
|
| 18781 |
\begin{align*}
y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.536 |
|
| 18782 |
\begin{align*}
t^{2} x^{\prime \prime }-t x^{\prime }+2 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.536 |
|
| 18783 |
\begin{align*}
{\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| 18784 |
\begin{align*}
y y^{\prime }+y^{4}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.539 |
|
| 18785 |
\begin{align*}
\frac {x y^{\prime }}{y}+2 \ln \left (y\right )&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.542 |
|
| 18786 |
\begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.542 |
|
| 18787 |
\begin{align*}
y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.543 |
|
| 18788 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-2 y&=\frac {t^{2}+1}{-t^{2}+1} \\
y \left (2\right ) &= y_{1} \\
y^{\prime }\left (2\right ) &= y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.544 |
|
| 18789 |
\begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.546 |
|
| 18790 |
\begin{align*}
x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.548 |
|
| 18791 |
\begin{align*}
3 r&=r^{\prime }-\theta ^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.549 |
|
| 18792 |
\begin{align*}
\left (20 x^{2}+8 y x +4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+y x +y^{2}+y^{3}\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.549 |
|
| 18793 |
\begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.549 |
|
| 18794 |
\begin{align*}
t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.552 |
|
| 18795 |
\begin{align*}
\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.553 |
|
| 18796 |
\begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.555 |
|
| 18797 |
\begin{align*}
x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.556 |
|
| 18798 |
\begin{align*}
\sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.560 |
|
| 18799 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.560 |
|
| 18800 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.561 |
|