| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15601 |
\begin{align*}
y^{\prime }&=\frac {y+x^{2}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.159 |
|
| 15602 |
\begin{align*}
{y^{\prime }}^{2}&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.160 |
|
| 15603 |
\begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.161 |
|
| 15604 |
\begin{align*}
y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.161 |
|
| 15605 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.161 |
|
| 15606 |
\begin{align*}
x^{\prime \prime }+16 x&=0 \\
x \left (0\right ) &= -2 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.163 |
|
| 15607 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| 15608 |
\begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.164 |
|
| 15609 |
\begin{align*}
y^{\prime \prime }+7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| 15610 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.164 |
|
| 15611 |
\begin{align*}
y^{\prime }&=y-{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| 15612 |
\begin{align*}
a y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| 15613 |
\begin{align*}
y^{\prime \prime }+\omega ^{2} y&=t \left (\sin \left (\omega t \right )+\cos \left (\omega t \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| 15614 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| 15615 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.166 |
|
| 15616 |
\begin{align*}
y^{2} \left (x^{2} y^{\prime \prime }-y^{\prime } x +y\right )&=x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.166 |
|
| 15617 |
\begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }-3 x&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.167 |
|
| 15618 |
\begin{align*}
m y^{\prime \prime }+a y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| 15619 |
\begin{align*}
y x +x^{2}-y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| 15620 |
\begin{align*}
y^{\prime \prime }-7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| 15621 |
\begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\
y \left (\frac {1}{4}\right ) &= 0 \\
y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.168 |
|
| 15622 |
\begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.170 |
|
| 15623 |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.170 |
|
| 15624 |
\begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.170 |
|
| 15625 |
\begin{align*}
y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.171 |
|
| 15626 |
\begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| 15627 |
\begin{align*}
y^{\prime }&=y+\frac {1}{1-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.171 |
|
| 15628 |
\begin{align*}
{y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.172 |
|
| 15629 |
\begin{align*}
-y+y^{\prime }&=t^{2}-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.172 |
|
| 15630 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.173 |
|
| 15631 |
\begin{align*}
y^{\prime \prime }+2 y&=x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.173 |
|
| 15632 |
\begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \\
y \left (1\right ) &= 1+\cos \left (2\right ) \\
y^{\prime }\left (1\right ) &= 4-2 \sin \left (2\right ) \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| 15633 |
\begin{align*}
y^{\prime \prime }&=\frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.174 |
|
| 15634 |
\begin{align*}
x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| 15635 |
\begin{align*}
x^{2}+y^{2}+y+\left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.174 |
|
| 15636 |
\begin{align*}
x -x^{2}-y^{2}+\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.174 |
|
| 15637 |
\begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -4\right )-\operatorname {Heaviside}\left (t -6\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| 15638 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.175 |
|
| 15639 |
\begin{align*}
x {y^{\prime }}^{2}+x y y^{\prime \prime }&=3 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.175 |
|
| 15640 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.176 |
|
| 15641 |
\begin{align*}
4 {y^{\prime }}^{3} x -6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.176 |
|
| 15642 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}+4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.177 |
|
| 15643 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x-3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| 15644 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=4 x^{2}+2 x +3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| 15645 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| 15646 |
\begin{align*}
y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.179 |
|
| 15647 |
\begin{align*}
\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.179 |
|
| 15648 |
\begin{align*}
-4 y x +x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.180 |
|
| 15649 |
\begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.181 |
|
| 15650 |
\begin{align*}
y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.181 |
|
| 15651 |
\begin{align*}
t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.181 |
|
| 15652 |
\begin{align*}
y^{\prime \prime }&=-m^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.181 |
|
| 15653 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.181 |
|
| 15654 |
\begin{align*}
y^{\prime } x +2 y&=\frac {\sin \left (x \right )}{x} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.182 |
|
| 15655 |
\begin{align*}
y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.182 |
|
| 15656 |
\begin{align*}
y^{\prime \prime }-y x -x^{3}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.183 |
|
| 15657 |
\begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= {\frac {1}{3}} \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.183 |
|
| 15658 |
\begin{align*}
y^{\prime \prime }+\left (b \,x^{3} a +b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.185 |
|
| 15659 |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.185 |
|
| 15660 |
\begin{align*}
y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.187 |
|
| 15661 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| 15662 |
\begin{align*}
y&=y {y^{\prime }}^{2}+2 y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| 15663 |
\begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.188 |
|
| 15664 |
\begin{align*}
y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.188 |
|
| 15665 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.188 |
|
| 15666 |
\begin{align*}
y^{\prime \prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.188 |
|
| 15667 |
\begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.188 |
|
| 15668 |
\begin{align*}
x^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.188 |
|
| 15669 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.189 |
|
| 15670 |
\begin{align*}
-2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=1+x +2 \ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| 15671 |
\begin{align*}
x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| 15672 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| 15673 |
\begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.191 |
|
| 15674 |
\begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.191 |
|
| 15675 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.192 |
|
| 15676 |
\begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.192 |
|
| 15677 |
\begin{align*}
2 y+y^{\prime } t&=\frac {\sin \left (t \right )}{t} \\
y \left (-\frac {\pi }{2}\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.193 |
|
| 15678 |
\begin{align*}
x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\
x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\
x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4} \\
x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.193 |
|
| 15679 |
\begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| 15680 |
\begin{align*}
a {y^{\prime }}^{2}+b y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| 15681 |
\begin{align*}
8 {y^{\prime }}^{3} x -12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.195 |
|
| 15682 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.195 |
|
| 15683 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.196 |
|
| 15684 |
\begin{align*}
y^{\prime \prime } x +y^{\prime } x -y&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.197 |
|
| 15685 |
\begin{align*}
\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 15686 |
\begin{align*}
y^{\prime } x +3 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 15687 |
\begin{align*}
-2 y+y^{\prime }&=\cos \left (\omega t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| 15688 |
\begin{align*}
y^{\prime }&=a y+b \\
y \left (c \right ) &= d \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| 15689 |
\begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| 15690 |
\begin{align*}
y^{\prime \prime }&=f \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.199 |
|
| 15691 |
\begin{align*}
-y+y^{\prime } x&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 15692 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| 15693 |
\begin{align*}
r r^{\prime }&=a \\
r \left (0\right ) &= b \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
2.200 |
|
| 15694 |
\begin{align*}
2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.201 |
|
| 15695 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 \left (a +x \right ) y^{\prime }}{x^{2}}-\frac {b y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.201 |
|
| 15696 |
\begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 15697 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 15698 |
\begin{align*}
y^{\prime }&=x^{2}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 15699 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x +3 y}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| 15700 |
\begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
2.202 |
|