| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 16101 |
\begin{align*}
y^{\prime \prime }+3 y&=-x^{6}+x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| 16102 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| 16103 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| 16104 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| 16105 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=-\frac {16 \ln \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| 16106 |
\begin{align*}
y^{\prime }&=\frac {1}{2 t -2 y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| 16107 |
\begin{align*}
y^{\prime } x&=x \sin \left (x \right )-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.498 |
|
| 16108 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.498 |
|
| 16109 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.498 |
|
| 16110 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=\sec \left (x \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.498 |
|
| 16111 |
\begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.499 |
|
| 16112 |
\begin{align*}
\frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| 16113 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| 16114 |
\begin{align*}
2 x -2 y^{2}+\left (12 y^{2}-4 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.500 |
|
| 16115 |
\begin{align*}
x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.500 |
|
| 16116 |
\begin{align*}
x^{\prime }&=c y-b z \\
y^{\prime }&=a z-c x \\
z^{\prime }&=b x-a y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| 16117 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| 16118 | \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 1.501 |
|
| 16119 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.501 |
|
| 16120 |
\begin{align*}
y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| 16121 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| 16122 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16123 |
\begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16124 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= {\frac {1}{9}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16125 |
\begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16126 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16127 |
\begin{align*}
y^{\prime } x +y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16128 |
\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. |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16129 |
\begin{align*}
y-3 x^{2}-\left (4 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.503 |
|
| 16130 |
\begin{align*}
y^{\prime \prime }+100 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| 16131 |
\begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| 16132 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| 16133 |
\begin{align*}
y^{\prime \prime }&=\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| 16134 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| 16135 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=1+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| 16136 |
\begin{align*}
3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| 16137 | \begin{align*}
2 y x -3+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.505 |
|
| 16138 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| 16139 |
\begin{align*}
3 \left (y-1\right ) x +y+2+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| 16140 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| 16141 |
\begin{align*}
y^{\prime }&=a +b \sin \left (A x +B y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| 16142 |
\begin{align*}
y^{\prime }&=y+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| 16143 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| 16144 |
\begin{align*}
y^{\prime }+3 x^{2} y&=x^{5} {\mathrm e}^{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| 16145 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 y+3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| 16146 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| 16147 |
\begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| 16148 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| 16149 |
\begin{align*}
y^{\prime \prime }&=t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| 16150 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.508 |
|
| 16151 |
\begin{align*}
y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.509 |
|
| 16152 |
\begin{align*}
\left (x -y^{2}\right ) y^{\prime }&=x^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.509 |
|
| 16153 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.509 |
|
| 16154 |
\begin{align*}
y^{\prime \prime }-y&=4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.509 |
|
| 16155 |
\begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.509 |
|
| 16156 |
\begin{align*}
\left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y}&={\mathrm e}^{-2 x} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.509 |
|
| 16157 | \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 1.510 |
|
| 16158 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| 16159 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| 16160 |
\begin{align*}
t y^{\prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| 16161 |
\begin{align*}
y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.511 |
|
| 16162 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x-3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.511 |
|
| 16163 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.511 |
|
| 16164 |
\begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.512 |
|
| 16165 |
\begin{align*}
y^{\prime }-3 z&=5 \\
y-z^{\prime }-x&=3-2 t \\
z+x^{\prime }&=-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| 16166 |
\begin{align*}
y^{\prime }&=y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.512 |
|
| 16167 |
\begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| 16168 |
\begin{align*}
r^{\prime }+r \tan \left (\theta \right )&=\sec \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| 16169 |
\begin{align*}
y&=\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.513 |
|
| 16170 |
\begin{align*}
-y+y^{\prime }&={\mathrm e}^{t} \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| 16171 |
\begin{align*}
y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.514 |
|
| 16172 |
\begin{align*}
y^{\prime \prime } x +y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.515 |
|
| 16173 |
\begin{align*}
y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.515 |
|
| 16174 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.516 |
|
| 16175 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| 16176 | \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.516 |
|
| 16177 |
\begin{align*}
y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.516 |
|
| 16178 |
\begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| 16179 |
\begin{align*}
y^{\prime }&=2 y x -x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| 16180 |
\begin{align*}
1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.517 |
|
| 16181 |
\begin{align*}
50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.517 |
|
| 16182 |
\begin{align*}
y^{\prime }&=\sqrt {\left (y+2\right ) \left (y-1\right )} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.517 |
|
| 16183 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\arcsin \left (\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.517 |
|
| 16184 |
\begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.518 |
|
| 16185 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.519 |
|
| 16186 |
\begin{align*}
\operatorname {a2} y+\operatorname {a1} \left (b x +a \right ) y^{\prime }+\left (b x +a \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.519 |
|
| 16187 |
\begin{align*}
x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\
x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\
x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| 16188 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| 16189 |
\begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| 16190 |
\begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| 16191 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| 16192 |
\begin{align*}
R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\
R \left (1\right ) &= 3 \ln \left (2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| 16193 |
\begin{align*}
w^{\prime }&=t w+t^{3} w^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| 16194 |
\begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| 16195 | \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 1.522 |
|
| 16196 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}+y}{y^{2}+x^{2}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.523 |
|
| 16197 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| 16198 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.523 |
|
| 16199 |
\begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| 16200 |
\begin{align*}
y^{\prime }&=\sqrt {y-x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.523 |
|