| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15101 |
\begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.195 |
|
| 15102 |
\begin{align*}
2 x^{\prime }-3 x-2 y^{\prime }&=t \\
2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.195 |
|
| 15103 |
\begin{align*}
x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.196 |
|
| 15104 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.196 |
|
| 15105 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.196 |
|
| 15106 |
\begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| 15107 |
\begin{align*}
x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2 \\
-2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| 15108 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| 15109 |
\begin{align*}
y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| 15110 |
\begin{align*}
y^{\prime } x&=x^{2}+y \left (1+y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| 15111 |
\begin{align*}
{y^{\prime }}^{2}&=x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| 15112 |
\begin{align*}
y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| 15113 |
\begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| 15114 |
\begin{align*}
2 \left (1-x \right ) x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| 15115 |
\begin{align*}
y_{1}^{\prime }&=y_{1} \\
y_{2}^{\prime }&=2 y_{1}+y_{4} \\
y_{3}^{\prime }&=y_{4} \\
y_{4}^{\prime }&=y_{2}+2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| 15116 |
\begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| 15117 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\
x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| 15118 | \begin{align*}
\left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 1.200 |
|
| 15119 |
\begin{align*}
y^{\prime \prime }-4 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| 15120 |
\begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| 15121 |
\begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.201 |
|
| 15122 |
\begin{align*}
y^{\prime } x +y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| 15123 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.202 |
|
| 15124 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.203 |
|
| 15125 |
\begin{align*}
\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.203 |
|
| 15126 |
\begin{align*}
x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.203 |
|
| 15127 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| 15128 |
\begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| 15129 |
\begin{align*}
y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.204 |
|
| 15130 |
\begin{align*}
4 y^{\prime \prime } x -\left (x +a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.204 |
|
| 15131 |
\begin{align*}
y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| 15132 |
\begin{align*}
y^{\prime }&=x -2 y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| 15133 |
\begin{align*}
4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.205 |
|
| 15134 |
\begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| 15135 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| 15136 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| 15137 |
\begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.206 |
|
| 15138 | \begin{align*}
y^{\prime \prime }+\omega ^{2} y&=\frac {F_{0} \cos \left (\omega t \right )}{m} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.207 |
|
| 15139 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| 15140 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| 15141 |
\begin{align*}
{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| 15142 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.207 |
|
| 15143 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (\infty \right ) &= a \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
1.207 |
|
| 15144 |
\begin{align*}
y^{\prime }&=2 y x +1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| 15145 |
\begin{align*}
y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.208 |
|
| 15146 |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} x^{2}+b x +c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.208 |
|
| 15147 |
\begin{align*}
x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t} \\
y^{\prime }-2 x-5 y+3 z&=0 \\
z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.208 |
|
| 15148 |
\begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| 15149 |
\begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| 15150 |
\begin{align*}
y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| 15151 |
\begin{align*}
y^{\prime \prime } x +\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.211 |
|
| 15152 |
\begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3}-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| 15153 |
\begin{align*}
t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| 15154 |
\begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| 15155 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| 15156 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| 15157 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| 15158 | \begin{align*}
y^{\prime }+2 y x&=1+x^{2}+y^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 1.213 |
|
| 15159 |
\begin{align*}
y^{\prime \prime } x +y^{\prime } x -y&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| 15160 |
\begin{align*}
y^{\prime \prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| 15161 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| 15162 |
\begin{align*}
y^{\prime } x +x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.213 |
|
| 15163 |
\begin{align*}
y&=\frac {3 y^{\prime } x}{2}+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| 15164 |
\begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 15165 |
\begin{align*}
y^{\prime \prime }+\frac {t^{2} y}{4}&=f \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.214 |
|
| 15166 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.214 |
|
| 15167 |
\begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 15168 |
\begin{align*}
y^{\prime \prime } x +\frac {y^{\prime }}{2}+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| 15169 |
\begin{align*}
T^{\prime }&=k \left (T-T_{m} \right ) \\
T \left (0\right ) &= T_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 15170 |
\begin{align*}
4 y^{\prime \prime }+8 y^{\prime }&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 15171 |
\begin{align*}
y^{\prime \prime }-9 y&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| 15172 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| 15173 |
\begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| 15174 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| 15175 |
\begin{align*}
z^{\prime }+y^{\prime }+5 y-3 z&=x +{\mathrm e}^{x} \\
y^{\prime }+2 y-z&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| 15176 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
y \left (1\right ) &= -3 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| 15177 | \begin{align*}
y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 1.218 |
|
| 15178 |
\begin{align*}
{b^{\prime }}^{7}&=3 p \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.218 |
|
| 15179 |
\begin{align*}
\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.219 |
|
| 15180 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 15181 |
\begin{align*}
y^{\prime \prime }-y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| 15182 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 15183 |
\begin{align*}
t^{2} y+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 15184 |
\begin{align*}
\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.220 |
|
| 15185 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 15186 |
\begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (1+3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| 15187 |
\begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 15188 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 15189 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 15190 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 15191 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 15192 |
\begin{align*}
x -y+2+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| 15193 |
\begin{align*}
y^{\prime } x +y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| 15194 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.223 |
|
| 15195 |
\begin{align*}
2 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.223 |
|
| 15196 | \begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 1.223 |
|
| 15197 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y p&=0 \\
\end{align*} Series expansion around \(x=0\). |
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✓ |
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1.223 |
|
| 15198 |
\begin{align*}
y^{\prime }-a y&=f \left (t \right ) \\
\end{align*} |
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1.223 |
|
| 15199 |
\begin{align*}
y^{\prime \prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
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1.224 |
|
| 15200 |
\begin{align*}
y^{\prime }&=x^{2}-2 y x +y^{2} \\
\end{align*} |
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1.224 |
|