| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15701 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| 15702 |
\begin{align*}
y y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.020 |
|
| 15703 |
\begin{align*}
u^{\prime \prime }+w_{0}^{2} u&=\cos \left (w t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| 15704 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y&=\left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| 15705 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=2 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| 15706 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.022 |
|
| 15707 |
\begin{align*}
y^{\prime }&=\left (1-y^{2}\right ) \left (4-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.022 |
|
| 15708 |
\begin{align*}
x^{3}+3 y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| 15709 |
\begin{align*}
y^{\prime }&=4 x -2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| 15710 |
\begin{align*}
x y^{\prime }-y&=x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| 15711 |
\begin{align*}
y^{\prime \prime }&=a \left (x y^{\prime }-y\right )^{k} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.025 |
|
| 15712 |
\begin{align*}
a y y^{\prime \prime }+b y&=c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.025 |
|
| 15713 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| 15714 |
\begin{align*}
t^{2} x^{\prime \prime }-x^{\prime } t -3 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| 15715 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| 15716 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=x \left (3 x^{3}+1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.027 |
|
| 15717 |
\begin{align*}
2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.027 |
|
| 15718 |
\begin{align*}
4 y x +2 x +\left (2 x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.027 |
|
| 15719 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.029 |
|
| 15720 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.029 |
|
| 15721 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.030 |
|
| 15722 |
\begin{align*}
y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| 15723 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+a y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.030 |
|
| 15724 |
\begin{align*}
y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.030 |
|
| 15725 |
\begin{align*}
y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -\sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| 15726 |
\begin{align*}
x^{2} y^{\prime }+3 y x&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.031 |
|
| 15727 |
\begin{align*}
x^{\prime \prime }&=2 t +1 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= -7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.032 |
|
| 15728 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| 15729 |
\begin{align*}
8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.033 |
|
| 15730 |
\begin{align*}
y^{\prime }&=\left (-1+y\right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| 15731 |
\begin{align*}
\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| 15732 |
\begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| 15733 |
\begin{align*}
2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.034 |
|
| 15734 |
\begin{align*}
y&=\frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.034 |
|
| 15735 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y-2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| 15736 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.035 |
|
| 15737 |
\begin{align*}
y y^{\prime }-\sqrt {a y^{2}+b}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.035 |
|
| 15738 |
\begin{align*}
-y-\left (-x^{2}+1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.036 |
|
| 15739 |
\begin{align*}
t^{2} x^{\prime }+3 x t&=t^{4} \ln \left (t \right )+1 \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| 15740 |
\begin{align*}
2 y-2 y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.037 |
|
| 15741 |
\begin{align*}
x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=c \,x^{2} \left (x -a \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.037 |
|
| 15742 |
\begin{align*}
\cos \left (x \right ) u^{\prime \prime }+\sin \left (x \right ) u^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) u&=0 \\
u \left (\frac {\pi }{4}\right ) &= 2 \\
u^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*}
Series expansion around \(x=\frac {\pi }{4}\). |
✓ |
✓ |
✓ |
✗ |
2.037 |
|
| 15743 |
\begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| 15744 |
\begin{align*}
\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| 15745 |
\begin{align*}
y^{\prime }+y&=\frac {1}{1+{\mathrm e}^{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| 15746 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| 15747 |
\begin{align*}
y^{\prime }&=k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.041 |
|
| 15748 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.041 |
|
| 15749 |
\begin{align*}
y^{\prime \prime }+y&=x^{2} \cos \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.041 |
|
| 15750 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+\left (3 a \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.043 |
|
| 15751 |
\begin{align*}
v^{\prime }+v&={\mathrm e}^{-s} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.043 |
|
| 15752 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=27 \,{\mathrm e}^{-6 x} \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.044 |
|
| 15753 |
\begin{align*}
\frac {x y^{\prime \prime }}{y+1}+\frac {y y^{\prime }-{y^{\prime }}^{2} x +y^{\prime }}{\left (y+1\right )^{2}}&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.044 |
|
| 15754 |
\begin{align*}
2 y y^{\prime \prime }&=-1+2 x f \left (x \right ) y^{2}-y^{4}-4 y^{2} y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.046 |
|
| 15755 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| 15756 |
\begin{align*}
y&=x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.046 |
|
| 15757 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.047 |
|
| 15758 |
\begin{align*}
x^{2} y y^{\prime \prime }+{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }&=4 y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.048 |
|
| 15759 |
\begin{align*}
{\mathrm e}^{x +y} y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| 15760 |
\begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.049 |
|
| 15761 |
\begin{align*}
y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| 15762 |
\begin{align*}
y^{\prime \prime }+9 y&=\frac {\csc \left (3 t \right )}{2} \\
y \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| 15763 |
\begin{align*}
3 y&=2 x y^{\prime }-\frac {2 {y^{\prime }}^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.049 |
|
| 15764 |
\begin{align*}
x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.050 |
|
| 15765 |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| 15766 |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.050 |
|
| 15767 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.050 |
|
| 15768 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.050 |
|
| 15769 |
\begin{align*}
y^{\prime }+x +y \cot \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| 15770 |
\begin{align*}
y^{\prime }&=-2 y+8 \\
y \left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| 15771 |
\begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.052 |
|
| 15772 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| 15773 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| 15774 |
\begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{-x}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.053 |
|
| 15775 |
\begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.054 |
|
| 15776 |
\begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 15777 |
\begin{align*}
y^{\prime }&=2 y \left (x \sqrt {y}-1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 15778 |
\begin{align*}
a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| 15779 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.056 |
|
| 15780 |
\begin{align*}
2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| 15781 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.058 |
|
| 15782 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=x \left (-x^{2}+1\right ) \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.059 |
|
| 15783 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 15784 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 15785 |
\begin{align*}
9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✗ |
2.059 |
|
| 15786 |
\begin{align*}
x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.059 |
|
| 15787 |
\begin{align*}
2 y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| 15788 |
\begin{align*}
y^{\prime \prime }+y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.060 |
|
| 15789 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| 15790 |
\begin{align*}
x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\
y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\
z^{\prime }&=-x+6 y+z+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| 15791 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.061 |
|
| 15792 |
\begin{align*}
y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 15793 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 15794 |
\begin{align*}
y^{\prime \prime }+\omega _{n}^{2} y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| 15795 |
\begin{align*}
y^{\prime }+4 y-{\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= {\frac {4}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 15796 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| 15797 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.065 |
|
| 15798 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.065 |
|
| 15799 |
\begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.065 |
|
| 15800 |
\begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.065 |
|