| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10101 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.768 |
|
| 10102 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10103 |
\begin{align*}
y^{\prime \prime } x +\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.768 |
|
| 10104 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\left (x^{2}+x \right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10105 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10106 |
\begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=2 x+3 y \\
z^{\prime }&=3 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10107 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10108 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10109 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=t \cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10110 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x+y+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10111 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10112 |
\begin{align*}
y^{\prime } \left (y^{\prime } x -y+k \right )+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10113 |
\begin{align*}
y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10114 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10115 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10116 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10117 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10118 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10119 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10120 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10121 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-x_{1}-3 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10122 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10123 |
\begin{align*}
x^{\prime }&=3 x-5 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10124 |
\begin{align*}
x^{\prime }&=5 x+9 y+2 \\
y^{\prime }&=-x+11 y+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10125 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.771 |
|
| 10126 |
\begin{align*}
y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\
y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10127 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=z-x \\
z^{\prime }&=x+3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10128 |
\begin{align*}
x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10129 |
\begin{align*}
y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.772 |
|
| 10130 |
\begin{align*}
16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| 10131 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10132 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=10 x^{3}-2 x +5 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| 10133 |
\begin{align*}
x^{\prime }-y^{\prime }&=x+y-t \\
2 x^{\prime }+3 y^{\prime }&=2 x+6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10134 |
\begin{align*}
x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| 10135 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10136 |
\begin{align*}
y^{\prime \prime }-y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10137 |
\begin{align*}
y^{\prime }&=\ln \left (x \right ) x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10138 |
\begin{align*}
2 y x -2 \left (x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10139 |
\begin{align*}
-\left (x^{2}+4 x +2\right ) y-\left (-x^{3}-3 x^{2}+2 x +2\right ) y^{\prime }+x \left (-x^{2}+2\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10140 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10141 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+\frac {y}{4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10142 |
\begin{align*}
2 x^{\prime }+y^{\prime }-3 x-y&=t \\
x^{\prime }+y^{\prime }-4 x-y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10143 |
\begin{align*}
2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t \\
x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10144 |
\begin{align*}
x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\
y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10145 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10146 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10147 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10148 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10149 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10150 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10151 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4-8 x +6 x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10152 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10153 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10154 |
\begin{align*}
y^{\prime \prime }-4 y&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10155 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10156 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10157 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10158 |
\begin{align*}
x^{\prime }&=x+y-5 t +2 \\
y^{\prime }&=4 x-2 y-8 t -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10159 |
\begin{align*}
s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10160 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{16}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10161 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 10162 |
\begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 10163 |
\begin{align*}
y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 10164 |
\begin{align*}
\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.775 |
|
| 10165 |
\begin{align*}
x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.775 |
|
| 10166 |
\begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.775 |
|
| 10167 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 \sin \left (3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 10168 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=-x+2 y-z \\
z^{\prime }&=-y+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 10169 |
\begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10170 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10171 |
\begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10172 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10173 |
\begin{align*}
\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10174 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10175 |
\begin{align*}
x^{\prime \prime }+2 x&=\cos \left (\sqrt {2}\, t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10176 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 10177 |
\begin{align*}
y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 10178 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+\sin \left (x \right ) y&=0 \\
y \left (0\right ) &= a_{0} \\
y^{\prime }\left (0\right ) &= a_{1} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10179 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10180 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10181 |
\begin{align*}
y^{\prime \prime }+i y^{\prime }+2 y&=2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10182 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.777 |
|
| 10183 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+A y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| 10184 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10185 |
\begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10186 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10187 |
\begin{align*}
y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10188 |
\begin{align*}
4 y+y^{\prime \prime }&=3 x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 10189 |
\begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10190 |
\begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.778 |
|
| 10191 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10192 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10193 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=6 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10194 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10195 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10196 |
\begin{align*}
x^{\prime }&=x-6 y \\
y^{\prime }&=-2 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10197 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 x} \sin \left (3 x \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -{\frac {25}{6}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 10198 |
\begin{align*}
y^{\prime \prime }-y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10199 |
\begin{align*}
\left (-y^{\prime } x +y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.779 |
|
| 10200 |
\begin{align*}
\left (x +3\right ) y-2 x \left (2+x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.779 |
|