| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7001 |
\begin{align*}
{y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7002 |
\begin{align*}
y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 \left (x +1\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.525 |
|
| 7003 |
\begin{align*}
\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.525 |
|
| 7004 |
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.525 |
|
| 7005 |
\begin{align*}
x y^{\prime \prime }+x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7006 |
\begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -21 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7007 |
\begin{align*}
5 y^{\prime \prime }+y^{\prime }-4 y&=-3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7008 |
\begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7009 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }-15 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7010 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7011 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7012 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7013 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| 7014 |
\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 1 & 0 & 3 \\ 0 & 0 & -2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.525 |
|
| 7015 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-4 x_{3} \\
x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7016 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.526 |
|
| 7017 |
\begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7018 |
\begin{align*}
{y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7019 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7020 |
\begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7021 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\
y \left (\frac {3}{2}\right ) &= 4 \\
y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7022 |
\begin{align*}
x y^{\prime }+y+3 x^{3} y^{4} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7023 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7024 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7025 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7026 |
\begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7027 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7028 |
\begin{align*}
y^{\prime }&=\frac {\sin \left (x \right )+x \cos \left (x \right )}{y \left (2 \ln \left (y\right )+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7029 |
\begin{align*}
y+y^{\prime }&=t \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7030 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }-3 y^{\prime }+\left (x -1\right ) y&=0 \\
y \left (1\right ) &= -20 \\
y^{\prime }\left (1\right ) &= -2 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7031 |
\begin{align*}
x^{\prime }&=-3 x+5 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7032 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }-2 y&=2+x +x \,{\mathrm e}^{-x}+x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7033 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime }+2 y&=-2 x^{4}+x^{2} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7034 |
\begin{align*}
4 y^{\prime \prime }+y&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7035 |
\begin{align*}
4 y^{\prime \prime }+y&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7036 |
\begin{align*}
{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7037 |
\begin{align*}
4 t^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7038 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=5 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{4 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| 7039 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7040 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7041 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+5 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7042 |
\begin{align*}
{y^{\prime }}^{2} x -\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7043 |
\begin{align*}
3 y-8 y^{\prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7044 |
\begin{align*}
2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7045 |
\begin{align*}
y^{\prime \prime }+d +b x y+c y+a y^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.527 |
|
| 7046 |
\begin{align*}
3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7047 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7048 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7049 |
\begin{align*}
y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7050 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7051 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7052 |
\begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{5 t} \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7053 |
\begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7054 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (x^{2}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7055 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7056 |
\begin{align*}
y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| 7057 |
\begin{align*}
x_{1}^{\prime }&=-6 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7058 |
\begin{align*}
x y^{\prime }&=x^{2}+2 x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7059 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7060 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7061 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7062 |
\begin{align*}
\left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7063 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7064 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| 7065 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7066 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7067 |
\begin{align*}
y^{\prime \prime }-2 x^{2} y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7068 |
\begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7069 |
\begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7070 |
\begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.529 |
|
| 7071 |
\begin{align*}
x y^{\prime \prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7072 |
\begin{align*}
\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7073 |
\begin{align*}
x^{\prime \prime }&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7074 |
\begin{align*}
y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.529 |
|
| 7075 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7076 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| 7077 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7078 |
\begin{align*}
-a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7079 |
\begin{align*}
\left (x +2\right ) y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7080 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (1\right ) &= {\mathrm e}^{2} \\
y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7081 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7082 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7083 |
\begin{align*}
y^{\prime \prime }+9 y&=\cos \left (3 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7084 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.530 |
|
| 7085 |
\begin{align*}
{y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7086 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }-\left (2 x^{3}-4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7087 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7088 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7089 |
\begin{align*}
y^{\prime }&=\frac {-10-2 x}{\left (x +2\right ) \left (x -4\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7090 |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7091 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7092 |
\begin{align*}
y^{\prime \prime }-3 y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| 7093 |
\begin{align*}
\left (6+4 x \right ) y^{\prime \prime }+\left (2 x +1\right ) y&=0 \\
y \left (-1\right ) &= -1 \\
y^{\prime }\left (-1\right ) &= 2 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 7094 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 7095 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 7096 |
\begin{align*}
x y^{\prime \prime }+v y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.531 |
|
| 7097 |
\begin{align*}
x^{\prime }&=-5 x+4 y \\
y^{\prime }&=2 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 7098 |
\begin{align*}
y^{\prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 7099 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| 7100 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.531 |
|