| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 7001 |
\begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.450 |
|
| 7002 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 7003 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 7004 |
\begin{align*}
x^{\prime }&=8 x-5 y \\
y^{\prime }&=16 x+8 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 7005 |
\begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 7006 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.450 |
|
| 7007 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 7008 |
\begin{align*}
y^{\prime \prime }+9 y&=\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| 7009 |
\begin{align*}
y^{\prime \prime }&=\left (x +y^{\prime }\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7010 |
\begin{align*}
x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| 7011 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| 7012 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7013 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✗ |
✗ |
0.451 |
|
| 7014 |
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.451 |
|
| 7015 |
\begin{align*}
x^{\prime }-3 x+2 y&=0 \\
y^{\prime }-x+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7016 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7017 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=-4 \cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7018 |
\begin{align*}
y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✗ |
0.451 |
|
| 7019 |
\begin{align*}
x^{\prime }&=x+y+{\mathrm e}^{t} \\
y^{\prime }&=x+y-{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7020 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| 7021 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7022 |
\begin{align*}
-a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.452 |
|
| 7023 |
\begin{align*}
x y^{5}+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.452 |
|
| 7024 |
\begin{align*}
5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.452 |
|
| 7025 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7026 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7027 |
\begin{align*}
\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7028 |
\begin{align*}
x^{\prime }&=y+z-x \\
y^{\prime }&=x-y+z \\
z^{\prime }&=x+y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7029 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7030 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7031 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=-2 c x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7032 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7033 |
\begin{align*}
4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7034 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7035 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| 7036 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7037 |
\begin{align*}
\left (-x +2\right ) y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= a_{0} \\
y^{\prime }\left (0\right ) &= a_{1} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7038 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=40 x^{3} \\
y \left (-1\right ) &= -1 \\
y^{\prime }\left (-1\right ) &= -7 \\
y^{\prime \prime }\left (-1\right ) &= -1 \\
y^{\prime \prime \prime }\left (-1\right ) &= -31 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7039 |
\begin{align*}
y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7040 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7041 |
\begin{align*}
2 y y^{\prime \prime }&=-a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.453 |
|
| 7042 |
\begin{align*}
y^{\prime \prime }&=y \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7043 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.453 |
|
| 7044 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7045 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7046 |
\begin{align*}
3 y^{\prime \prime }+48 y^{\prime }+192 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7047 |
\begin{align*}
x^{6} y^{\left (6\right )}-12 x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7048 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7049 |
\begin{align*}
4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7050 |
\begin{align*}
y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\
y \left (2\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7051 |
\begin{align*}
y^{\prime \prime }+4 y&=1+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7052 |
\begin{align*}
y_{1}^{\prime }-y_{1}&=-2 y_{2} \\
y_{2}^{\prime }-y_{2}&=2 y_{1} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7053 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7054 |
\begin{align*}
y^{\prime \prime }-y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| 7055 |
\begin{align*}
4 y^{\prime \prime } x +8 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7056 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7057 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (2 x^{2}+3\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7058 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7059 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7060 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+4 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 3 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7061 |
\begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
x-y^{\prime }+2 y&=3 \,{\mathrm e}^{4 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7062 |
\begin{align*}
\left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.454 |
|
| 7063 |
\begin{align*}
4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7064 |
\begin{align*}
16 \left (x +1\right )^{2} y^{\prime \prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.454 |
|
| 7065 |
\begin{align*}
y^{\prime \prime }+9 y&=-3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7066 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \sin \left (x \right )-2 \cos \left (x \right ) x \right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.454 |
|
| 7067 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7068 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7069 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y&=x^{3}-3 x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7070 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7071 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.454 |
|
| 7072 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7073 |
\begin{align*}
5 y^{\prime \prime }+10 y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7074 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| 7075 |
\begin{align*}
f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7076 |
\begin{align*}
x^{\prime }&=7 x-5 y \\
y^{\prime }&=10 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7077 |
\begin{align*}
y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.455 |
|
| 7078 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=x \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7079 |
\begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=2 x-6 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7080 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7081 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7082 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7083 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=t \,{\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| 7084 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=13 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7085 |
\begin{align*}
\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7086 |
\begin{align*}
3 \left (1-y\right ) y y^{\prime \prime }&=2 \left (1-2 y\right ) {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| 7087 |
\begin{align*}
-y+y^{\prime } x&=x^{3} \cos \left (x \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7088 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7089 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=n^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7090 |
\begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7091 |
\begin{align*}
x^{\prime }&=1+x \\
y^{\prime }&=x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7092 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| 7093 |
\begin{align*}
y^{\prime }&=y-3 z \\
z^{\prime }&=2 y-4 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| 7094 |
\begin{align*}
y&=y^{\prime } x -\frac {1}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| 7095 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x+2 y-{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| 7096 |
\begin{align*}
x_{1}^{\prime }&=x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 10 \\
x_{2} \left (0\right ) &= 12 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| 7097 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| 7098 |
\begin{align*}
x^{\prime }&=1-\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| 7099 |
\begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| 7100 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.457 |
|