| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9001 |
\begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9002 |
\begin{align*}
2 y+2 \left (1-x \right ) y^{\prime }+\left (-x +2\right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 9003 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9004 |
\begin{align*}
y^{\prime }-y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9005 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9006 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9007 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9008 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}-x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 9009 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 9010 |
\begin{align*}
x^{\prime }&=-3 x-y \\
y^{\prime }&=4 x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9011 |
\begin{align*}
x&=\left (x^{2}-9\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9012 |
\begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 9013 |
\begin{align*}
v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9014 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9015 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=2 t \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 9016 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +3 y&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 9017 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 9018 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 7 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9019 |
\begin{align*}
2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9020 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=-8 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9021 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9022 |
\begin{align*}
-\left (x +1\right ) y+x \left (3-5 x \right ) y^{\prime }+2 \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| 9023 |
\begin{align*}
y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9024 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| 9025 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9026 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9027 |
\begin{align*}
x^{\prime }&=y-x+{\mathrm e}^{t} \\
y^{\prime }&=x-y+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9028 |
\begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=a x+\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9029 |
\begin{align*}
y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9030 |
\begin{align*}
2 y^{\prime \prime }+4 y&={\mathrm e}^{i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9031 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 9032 |
\(\left [\begin {array}{cc} 1 & -6 \\ 2 & 2 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.550 |
|
| 9033 |
\begin{align*}
\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9034 |
\begin{align*}
\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9035 |
\begin{align*}
\left (x^{2}-3 x +2\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9036 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=-2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9037 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 31 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9038 |
\begin{align*}
y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9039 |
\begin{align*}
x^{\prime }&=2 x-\frac {5 y}{2} \\
y^{\prime }&=\frac {9 x}{5}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9040 |
\begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9041 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9042 |
\begin{align*}
y^{\prime }-2 y-v^{\prime }-v&=6 \,{\mathrm e}^{3 x} \\
2 y^{\prime }-3 y+v^{\prime }-3 v&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.551 |
|
| 9043 |
\begin{align*}
y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.551 |
|
| 9044 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )+\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9045 |
\begin{align*}
x^{\prime \prime \prime }-x^{\prime \prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 3 \\
x^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 9046 |
\begin{align*}
a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 9047 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9048 |
\begin{align*}
2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9049 |
\begin{align*}
y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9050 |
\begin{align*}
2 y+3 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 9051 |
\begin{align*}
4 y-2 y^{\prime }+y^{\prime \prime \prime }&=\cos \left (x \right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9052 |
\begin{align*}
x^{3} \left (y^{\prime }-x \right )&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9053 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 9054 |
\begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9055 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9056 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9057 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9058 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9059 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=2 x^{3}+7 x^{2}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9060 |
\begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9061 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=3+x \,{\mathrm e}^{x}+x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| 9062 |
\begin{align*}
4 y^{\prime } x +2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.552 |
|
| 9063 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9064 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9065 |
\begin{align*}
y^{\prime }-2 y&=x y^{3} \\
y \left (0\right ) &= 2 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9066 |
\begin{align*}
\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9067 |
\begin{align*}
w^{\prime }+w x&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9068 |
\(\left [\begin {array}{cc} 0 & 1 \\ -1 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.553 |
|
| 9069 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9070 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&={\mathrm e}^{-2 t} \sin \left (4 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9071 |
\begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.553 |
|
| 9072 |
\begin{align*}
\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.553 |
|
| 9073 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9074 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9075 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9076 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=-{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9077 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=-5 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| 9078 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )+\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9079 |
\begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9080 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9081 |
\begin{align*}
\left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9082 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9083 |
\begin{align*}
x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9084 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9085 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9086 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9087 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| 9088 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9089 |
\begin{align*}
4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9090 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9091 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-6\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.555 |
|
| 9092 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=-4 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9093 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.555 |
|
| 9094 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9095 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9096 |
\begin{align*}
y^{\prime \prime }+y&=x \,{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9097 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9098 |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9099 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=6 \delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| 9100 |
\begin{align*}
2 y^{\prime \prime } x +3 y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.556 |
|