| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9101 |
\begin{align*}
4 y+y^{\prime \prime }&=\sinh \left (x \right ) \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9102 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 9103 |
\begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 9104 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 9105 |
\begin{align*}
y_{1}^{\prime }&=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*} |
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| 9106 |
\begin{align*}
x^{2} \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )+x y y^{\prime }&=\left (2 x y^{\prime }-3 y\right ) \sqrt {x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.670 |
|
| 9107 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9108 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9109 |
\begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.671 |
|
| 9110 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9111 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{1-x}+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9112 |
\begin{align*}
y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.671 |
|
| 9113 |
\begin{align*}
x y^{\prime \prime }+a y^{\prime }+b \,x^{n} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.671 |
|
| 9114 |
\begin{align*}
\left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-\sin \left (t \right ) x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.671 |
|
| 9115 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=25 \sin \left (6 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9116 |
\begin{align*}
y^{\prime }&=\left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9117 |
\begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9118 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }-6 y&=3 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9119 |
\begin{align*}
x^{\prime }&=3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9120 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9121 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+x^{2} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9122 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 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 ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9123 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9124 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9125 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=10 \,{\mathrm e}^{-x}+8 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9126 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9127 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-6 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9128 |
\begin{align*}
x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9129 |
\begin{align*}
y^{\prime \prime }+5 y&=\cos \left (\sqrt {5}\, x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9130 |
\begin{align*}
y^{\prime \prime }+9 y&=-3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9131 |
\begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9132 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9133 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=t +2 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9134 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9135 |
\begin{align*}
x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9136 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9137 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \left (2 x +\sin \left (2 x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9138 |
\begin{align*}
x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\
x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\
x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9139 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9140 |
\begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9141 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }-4 x&=2 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9142 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9143 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=3 t \\
y \left (0\right ) &= {\frac {23}{12}} \\
y^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9144 |
\begin{align*}
y^{\prime \prime }+4 y&=\tan \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9145 |
\begin{align*}
y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.673 |
|
| 9146 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.673 |
|
| 9147 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=6 x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9148 |
\begin{align*}
x^{\prime }&=1+x \\
y^{\prime }&=x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9149 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9150 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=20-3 x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9151 |
\begin{align*}
x y^{\prime }+6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9152 |
\begin{align*}
x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\
x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\
x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9153 |
\begin{align*}
u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5}&=\cos \left (t \right ) \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.674 |
|
| 9154 |
\begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \\
x^{\prime }+y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9155 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 \cosh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| 9156 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
y \left (0\right ) &= {\frac {101}{100}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9157 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9158 |
\begin{align*}
x y y^{\prime \prime }-{y^{\prime }}^{2} x +a y y^{\prime }+b x y^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.674 |
|
| 9159 |
\begin{align*}
y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9160 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=4 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9161 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9162 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9163 |
\begin{align*}
x^{\prime }-2 y^{\prime }&={\mathrm e}^{t} \\
x^{\prime }+y^{\prime }&=\sqrt {t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9164 |
\begin{align*}
y^{\prime }&=x +2 z \\
z^{\prime }&=3 x +y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9165 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.674 |
|
| 9166 |
\begin{align*}
x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\
x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\
x_{3}^{\prime }&=\frac {x_{3}}{10} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9167 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9168 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9169 |
\begin{align*}
\left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 9170 |
\begin{align*}
1+y^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9171 |
\begin{align*}
y^{\prime \prime }&=k \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9172 |
\begin{align*}
x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9173 |
\begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9174 |
\begin{align*}
9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9175 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 9176 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9177 |
\begin{align*}
y^{\prime }&=2 y-5 z \\
z^{\prime }&=4 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9178 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9179 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{-5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9180 |
\(\left [\begin {array}{cccc} 5 & 1 & 0 & 9 \\ 0 & 1 & 0 & 9 \\ 0 & 0 & 0 & 9 \\ 0 & 0 & 0 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.675 |
|
| 9181 |
\begin{align*}
y^{\prime }&=1+3 y \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 9182 |
\begin{align*}
y {y^{\prime }}^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 9183 |
\begin{align*}
x^{\prime }&=8 x+14 y \\
y^{\prime }&=7 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 9184 |
\begin{align*}
y^{\prime }-3 y&=\delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 9185 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9186 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9187 |
\begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9188 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}-2 y_{2} \\
y_{2}^{\prime }&=y_{2}-y_{1} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9189 |
\begin{align*}
y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9190 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9191 |
\begin{align*}
2 x-y^{\prime }-5 y&=0 \\
x^{\prime }+x+2 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9192 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9193 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9194 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \\
\end{align*} |
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✓ |
✓ |
✓ |
0.677 |
|
| 9195 |
\begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9196 |
\begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=x_{1}+5 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{2}-2 x_{3} \\
\end{align*} |
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✓ |
✓ |
0.678 |
|
| 9197 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=x_{2}-8 x_{3} \\
x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\
\end{align*} |
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✓ |
✓ |
✓ |
0.678 |
|
| 9198 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
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✓ |
✓ |
✓ |
0.678 |
|
| 9199 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 9200 |
\begin{align*}
\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (t +1\right ) x^{\prime }-\left (t -2\right ) x&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|