| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8101 |
\begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.406 |
|
| 8102 |
\begin{align*}
\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x}&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.406 |
|
| 8103 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8104 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+y&=t^{2}+3 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8105 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8106 |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{k t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8107 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8108 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.406 |
|
| 8109 |
\begin{align*}
y_{1}^{\prime }&=2 y_{2} \\
y_{2}^{\prime }&=-2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8110 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8111 |
\begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&={\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| 8112 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8113 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8114 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8115 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8116 |
\begin{align*}
4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8117 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8118 | \begin{align*}
y^{\prime }&=y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.407 |
|
| 8119 |
\begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8120 |
\begin{align*}
y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.407 |
|
| 8121 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8122 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8123 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8124 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8125 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8126 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8127 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| 8128 |
\begin{align*}
x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8129 |
\begin{align*}
\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\
y \left (4\right ) &= 3 \\
y^{\prime }\left (4\right ) &= -4 \\
\end{align*} Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8130 |
\begin{align*}
2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8131 |
\begin{align*}
16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y&=96 x^{{5}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8132 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=40 x^{3} \\
y \left (-1\right ) &= -1 \\
y^{\prime }\left (-1\right ) &= -7 \\
y^{\prime \prime }\left (-1\right ) &= -1 \\
y^{\prime \prime \prime }\left (-1\right ) &= -31 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8133 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8134 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8135 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8136 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.408 |
|
| 8137 | \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.408 |
|
| 8138 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8139 |
\begin{align*}
\left (-x^{2}+2\right ) y+4 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8140 |
\begin{align*}
-\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8141 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8142 |
\begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8143 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.408 |
|
| 8144 |
\begin{align*}
\left (y-1\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8145 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8146 |
\begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8147 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8148 |
\begin{align*}
y^{\prime \prime }&=\frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.408 |
|
| 8149 |
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.408 |
|
| 8150 |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8151 |
\begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8152 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 14 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8153 |
\begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8154 |
\begin{align*}
y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8155 |
\begin{align*}
x^{\prime }&=8 y-x \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8156 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 4 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8157 | \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.408 |
|
| 8158 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8159 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8160 |
\begin{align*}
\left (y^{2}+x^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.408 |
|
| 8161 |
\begin{align*}
y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8162 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| 8163 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8164 |
\begin{align*}
\left (3 x +2\right ) y^{\prime \prime }-y^{\prime } x +2 y x&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8165 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=169 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8166 |
\begin{align*}
\left (-2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8167 |
\begin{align*}
2 x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.409 |
|
| 8168 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8169 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8170 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8171 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8172 |
\begin{align*}
y^{\prime \prime }+2 y&=7 \cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8173 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| 8174 |
\begin{align*}
x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\
x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8175 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8176 | \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{3} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.410 |
|
| 8177 |
\begin{align*}
x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8178 |
\begin{align*}
\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8179 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=x^{2}+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8180 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=10 \sin \left (4 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8181 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.410 |
|
| 8182 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.410 |
|
| 8183 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8184 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8185 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8186 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8187 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8188 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+5 y&=4 \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8189 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-6 t y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8190 |
\begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| 8191 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| 8192 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| 8193 |
\begin{align*}
y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| 8194 |
\begin{align*}
9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| 8195 | \begin{align*}
t \left (2-t \right ) y^{\prime \prime }-6 \left (-1+t \right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(t=1\). | ✓ | ✓ | ✓ | ✓ | 0.411 |
|
| 8196 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| 8197 |
\begin{align*}
y^{\prime \prime }+y&=3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| 8198 |
\begin{align*}
\left (\left (-a +1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (-a +1\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.411 |
|
| 8199 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.411 |
|
| 8200 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.411 |
|