| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 5001 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y x&=2+x \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.391 |
|
| 5002 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| 5003 |
\begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=2 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5004 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=-7 x_{1}+9 x_{2}+7 x_{3} \\
x_{3}^{\prime }&=2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5005 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{3} \\
x_{2}^{\prime }&=x_{2}-4 x_{3} \\
x_{3}^{\prime }&=x_{2}-3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5006 |
\begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| 5007 |
\begin{align*}
\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| 5008 |
\begin{align*}
\sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| 5009 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+p x y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5010 |
\begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5011 |
\begin{align*}
\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5012 |
\begin{align*}
x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 y^{\prime \prime } x -8 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5013 |
\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.392 |
|
| 5014 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (1\right ) &= 0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5015 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| 5016 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5017 |
\begin{align*}
y^{\prime \prime }&=x^{2} y-y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5018 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-5 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5019 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5020 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| 5021 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5022 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +t^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5023 |
\begin{align*}
y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5024 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5025 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5026 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5027 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5028 |
\begin{align*}
x^{\prime }&=-2 x-2 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*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5029 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5030 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5031 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=-\sec \left (t \right ) \tan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5032 |
\begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5033 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5034 |
\begin{align*}
y^{\prime }-7 y&=-x^{4}+2 \\
y \left (0\right ) &= a \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| 5035 |
\begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5036 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=4 x^{4} \\
y \left (-1\right ) &= 7 \\
y^{\prime }\left (-1\right ) &= -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5037 |
\begin{align*}
x_{1}^{\prime }&=-5 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5038 |
\begin{align*}
y^{\prime \prime }-y&=6 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5039 |
\begin{align*}
2 y^{\prime } \left (1+y^{\prime }\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.394 |
|
| 5040 |
\begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=-x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5041 |
\begin{align*}
3 \left (x +3\right ) x^{2} y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.394 |
|
| 5042 |
\begin{align*}
\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.394 |
|
| 5043 |
\begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=2 x-5 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5044 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5045 |
\begin{align*}
x^{\prime }&=x-4 y \\
y^{\prime }&=4 x-7 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5046 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| 5047 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5048 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5049 |
\begin{align*}
2 y^{3}+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5050 |
\begin{align*}
x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5051 |
\begin{align*}
x^{\prime }&=1-\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5052 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5053 |
\begin{align*}
y^{\prime }-{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5054 |
\begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
y \left (0\right ) &= {\frac {101}{100}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5055 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.395 |
|
| 5056 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5057 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5058 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5059 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5060 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| 5061 |
\begin{align*}
t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.395 |
|
| 5062 |
\begin{align*}
\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5063 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5064 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5065 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5066 |
\begin{align*}
-y+y^{\prime }&=5 \sin \left (2 t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5067 |
\begin{align*}
y^{\prime } t +y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5068 |
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.396 |
|
| 5069 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }+t y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5070 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5071 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5072 |
\begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| 5073 |
\begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t +y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| 5074 |
\begin{align*}
y^{\prime }&=y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| 5075 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.397 |
|
| 5076 |
\begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=-3 x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| 5077 |
\begin{align*}
y^{\prime }+\left (2+x \right ) y^{\prime \prime }+\left (2+x \right )^{2} y^{\prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.397 |
|
| 5078 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 10 \\
y^{\prime \prime }\left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| 5079 |
\begin{align*}
y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.397 |
|
| 5080 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| 5081 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| 5082 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5083 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{2}-x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5084 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5085 |
\begin{align*}
y^{\prime \prime } x&=-y^{2}-2 y^{\prime }+x^{2} {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.398 |
|
| 5086 |
\begin{align*}
2 y x +\left (y^{2}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5087 |
\begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5088 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100 \\
y \left (2\right ) &= -4 \\
y^{\prime }\left (2\right ) &= 14 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5089 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y&=f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5090 |
\begin{align*}
-2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5091 |
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.398 |
|
| 5092 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5093 |
\begin{align*}
x^{\prime }&=9 y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5094 |
\begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.398 |
|
| 5095 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x&=17 x^{6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5096 |
\begin{align*}
x^{\prime }&=8 x+y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5097 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5098 |
\begin{align*}
y^{\prime \prime }+4 y&=4 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5099 |
\begin{align*}
y_{1}^{\prime }&=2 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*} |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| 5100 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.399 |
|