| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9001 |
\begin{align*}
\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| 9002 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| 9003 |
\begin{align*}
x^{\prime }&=-3 x+\sqrt {2}\, y \\
y^{\prime }&=\sqrt {2}\, x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| 9004 |
\begin{align*}
y^{2}-2 \sin \left (2 t \right )+\left (1+2 y t \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| 9005 |
\begin{align*}
x^{\prime }&=8 y-x \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| 9006 |
\begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| 9007 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| 9008 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x} \ln \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| 9009 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-\left (x -1\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9010 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }&=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9011 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9012 |
\begin{align*}
\left (x +1\right ) y^{\prime }-n y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9013 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9014 |
\begin{align*}
x^{\prime }&=5 x-y \\
y^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9015 |
\begin{align*}
x^{\prime \prime }-x&=t \\
x \left (0\right ) &= 0 \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9016 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9017 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9018 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2}+2 t \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+5 \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 13 \\
x_{2} \left (0\right ) &= 12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| 9019 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.662 |
|
| 9020 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| 9021 |
\begin{align*}
8 y^{\prime \prime }-y&=x \,{\mathrm e}^{-\frac {x}{2}} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| 9022 |
\begin{align*}
2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.663 |
|
| 9023 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| 9024 |
\begin{align*}
x^{\prime }&=9 y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| 9025 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| 9026 |
\begin{align*}
x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| 9027 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9028 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x^{2}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9029 |
\begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9030 |
\begin{align*}
x y y^{\prime \prime }-2 {y^{\prime }}^{2} x +\left (y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.664 |
|
| 9031 |
\begin{align*}
2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.664 |
|
| 9032 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9033 |
\begin{align*}
x y^{\prime }+2&=\sqrt {x} \\
y \left (1\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9034 |
\begin{align*}
3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9035 |
\begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9036 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+24 y&=f \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| 9037 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9038 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9039 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9040 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9041 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9042 |
\begin{align*}
x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t} \\
x+y^{\prime }-y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9043 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=6 y_{1}+y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9044 |
\begin{align*}
\left (x^{2}-3 x +2\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9045 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9046 |
\begin{align*}
x^{\prime }&=x+4 y \\
y^{\prime }&=-3 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9047 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9048 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9049 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| 9050 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| 9051 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+\frac {y}{16}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| 9052 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9053 |
\begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9054 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9055 |
\begin{align*}
x y^{\prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9056 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9057 |
\begin{align*}
x^{\prime }-x+2 y^{\prime }+7 y&=0 \\
2 x^{\prime }+y^{\prime }+x+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9058 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}-{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| 9059 |
\begin{align*}
x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.666 |
|
| 9060 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9061 |
\begin{align*}
y^{\prime }&=x +\frac {1}{x} \\
y \left (-2\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9062 |
\begin{align*}
y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9063 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9064 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9065 |
\begin{align*}
y^{\prime \prime }+y&=-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9066 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9067 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9068 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9069 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9070 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9071 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=18 \cos \left (3 x \right ) {\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9072 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9073 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| 9074 |
\begin{align*}
y^{\prime \prime }&=\left (x +y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9075 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-6 x_{1}-x_{2} \\
x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9076 |
\begin{align*}
3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9077 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9078 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9079 |
\begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 9080 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 9081 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9082 |
\begin{align*}
y^{\prime }&=-x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9083 |
\begin{align*}
y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 9084 |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (-3 x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9085 |
\begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 9086 |
\begin{align*}
y^{\prime \prime }-\left (x -1\right ) y^{\prime }&=x^{2}-2 x \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 9087 |
\begin{align*}
4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9088 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9089 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=-x+2 y-z \\
z^{\prime }&=-y+3 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9090 |
\begin{align*}
y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| 9091 |
\begin{align*}
x \left (x +4\right ) y^{\prime \prime }-\left (2 x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| 9092 |
\begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9093 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9094 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9095 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9096 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9097 |
\begin{align*}
\frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9098 |
\begin{align*}
4 y+y^{\prime \prime }&=-8+2 x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9099 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| 9100 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.669 |
|