| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12101 |
\begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.003 |
|
| 12102 |
\begin{align*}
x^{\prime \prime }-\frac {x^{\prime }}{t}&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12103 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12104 |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12105 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| 12106 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12107 |
\begin{align*}
x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12108 |
\begin{align*}
y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| 12109 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12110 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2}+t \,{\mathrm e}^{-2 t} \\
x_{2}^{\prime }&=3 x_{1}-5 x_{2}+t \,{\mathrm e}^{-2 t} \\
x_{3}^{\prime }&=4 x_{1}+7 x_{2}-2 x_{3}+t^{2} {\mathrm e}^{-2 t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 6 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| 12111 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.005 |
|
| 12112 |
\begin{align*}
x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}}&=0 \\
\end{align*}
Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12113 |
\begin{align*}
x&=y^{\prime \prime }+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12114 |
\begin{align*}
t y^{\prime \prime }+2 y^{\prime }+9 y t&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12115 |
\begin{align*}
x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| 12116 |
\begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12117 |
\begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.006 |
|
| 12118 |
\begin{align*}
y^{\prime }&=2 y-4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12119 |
\begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+2 z \\
z^{\prime }&=2 y+5 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12120 |
\begin{align*}
\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.006 |
|
| 12121 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12122 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}+x_{2}+3 x_{3}+3 t \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12123 |
\begin{align*}
y^{\prime \prime }+3 y&=\sin \left (x \right )+\frac {\sin \left (3 x \right )}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| 12124 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12125 |
\begin{align*}
4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12126 |
\begin{align*}
{y^{\prime }}^{2} x +\left (a -y\right ) y^{\prime }+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 12127 |
\begin{align*}
-\left (x +1\right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 12128 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=x^{3}+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12129 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12130 |
\begin{align*}
y y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 12131 |
\begin{align*}
\left (x y^{\prime }-y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| 12132 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12133 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12134 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=10 \sin \left (x \right )+17 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12135 |
\begin{align*}
y^{\prime \prime }+y&=4 x \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12136 |
\begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12137 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12138 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+4 y t&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12139 |
\begin{align*}
4 y^{\prime \prime }+B y^{\prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| 12140 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\
x_{2}^{\prime }&=-x_{1}-2 x_{2}+x_{3}+t \\
x_{3}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12141 |
\begin{align*}
x^{\prime }&=2 x-y+{\mathrm e}^{t} \\
y^{\prime }&=3 x-2 y+t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| 12142 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12143 |
\begin{align*}
4 t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12144 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12145 |
\begin{align*}
a \,x^{2} y+2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12146 |
\begin{align*}
\left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.009 |
|
| 12147 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=18 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12148 |
\begin{align*}
x^{\prime }&=-4 x+2 y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12149 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12150 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| 12151 |
\begin{align*}
3 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12152 |
\begin{align*}
x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12153 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12154 |
\begin{align*}
y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12155 |
\begin{align*}
7 y^{\prime \prime }-y^{\prime }&=14 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| 12156 |
\begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y&={\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.011 |
|
| 12157 |
\begin{align*}
y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12158 |
\begin{align*}
x^{\prime }&=-11 x-2 y \\
y^{\prime }&=13 x-9 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12159 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=\cos \left (x \right )+2 \delta \left (x -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.011 |
|
| 12160 |
\begin{align*}
y^{\prime \prime }&=x +\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12161 |
\begin{align*}
y^{\prime \prime }+y \,{\mathrm e}^{x}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12162 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| 12163 |
\begin{align*}
4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12164 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12165 |
\begin{align*}
y^{\prime }-3 y&=6 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12166 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12167 |
\begin{align*}
3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.012 |
|
| 12168 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| 12169 |
\begin{align*}
4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12170 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \left (1+\cos \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12171 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12172 |
\begin{align*}
x^{\prime }&=x+y-3 \\
y^{\prime }&=-x+y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12173 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{1}+2 x_{2}+2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-3 x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12174 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 12175 |
\begin{align*}
4 y+y^{\prime \prime }&=12 \sin \left (x \right )+12 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12176 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\frac {2 x^{3}+x^{2}-4 x -6}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| 12177 |
\begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| 12178 |
\begin{align*}
x^{\prime }+y^{\prime }+x&=0 \\
x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12179 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12180 |
\begin{align*}
y^{\prime \prime }-4 y&=x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12181 |
\begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=-y_{1} \\
y_{3}^{\prime }&=y_{1}+4 y_{2}-y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12182 |
\begin{align*}
y^{\prime }&=y \ln \left (y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| 12183 |
\begin{align*}
3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12184 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.015 |
|
| 12185 |
\begin{align*}
x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t} \\
y^{\prime }&=2 x-10 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12186 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12187 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| 12188 |
\begin{align*}
x y^{\prime \prime }+x&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12189 |
\begin{align*}
x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (1-n \right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (1-n \right ) x y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12190 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| 12191 |
\begin{align*}
x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.016 |
|
| 12192 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 12193 |
\begin{align*}
x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12194 |
\begin{align*}
a \,{\mathrm e}^{-1+y}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.017 |
|
| 12195 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 12196 |
\begin{align*}
x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| 12197 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=1 \\
x^{\prime }+y^{\prime }+2 x-y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12198 |
\begin{align*}
x^{\prime }&=-3 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12199 |
\begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| 12200 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.017 |
|