| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 5101 |
\begin{align*}
x^{2} y^{\prime \prime }&=12 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5102 |
\begin{align*}
-2 y-x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5103 |
\begin{align*}
\sqrt {y}\, y^{\prime \prime }&=2 b x +2 a \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.348 |
|
| 5104 |
\begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5105 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5106 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5107 |
\begin{align*}
y^{\prime \prime }&=\frac {1}{x} \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.348 |
|
| 5108 |
\begin{align*}
y^{\prime \prime }+y&=x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5109 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5110 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.348 |
|
| 5111 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.348 |
|
| 5112 |
\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.348 |
|
| 5113 |
\begin{align*}
\left (x^{2}+1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5114 |
\begin{align*}
x^{2} y^{\prime \prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5115 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5116 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5117 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5118 |
\begin{align*}
y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5119 |
\begin{align*}
y^{\prime \prime }+y&=x \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5120 |
\begin{align*}
y^{\prime \prime \prime \prime }&=\ln \left (x \right ) \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
y^{\prime \prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5121 |
\begin{align*}
x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 y^{\prime } x -18 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5122 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| 5123 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2-\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5124 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5125 |
\begin{align*}
x^{\prime }+2 y^{\prime }&=4 x+5 y \\
2 x^{\prime }-y^{\prime }&=3 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5126 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5127 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5128 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5129 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5130 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5131 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5132 |
\begin{align*}
y^{\prime \prime }+2 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5133 |
\begin{align*}
y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-y f^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5134 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5135 |
\begin{align*}
t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.349 |
|
| 5136 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.349 |
|
| 5137 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
y^{\prime \prime \prime }\left (0\right ) &= -60 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5138 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5139 |
\begin{align*}
y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5140 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5141 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5142 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5143 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= -4 \\
y^{\prime \prime \prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5144 |
\begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5145 |
\begin{align*}
y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5146 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5147 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5148 |
\begin{align*}
y^{\prime \prime }-y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5149 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5150 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| 5151 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5152 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5153 |
\begin{align*}
y_{1}^{\prime }&=y_{2} \\
y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5154 |
\begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 5155 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5156 |
\begin{align*}
y^{\prime \prime }+c y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5157 |
\begin{align*}
x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 5158 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 5159 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5160 |
\begin{align*}
b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 5161 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| 5162 |
\begin{align*}
y^{\prime \prime }-9 y&=2+x \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5163 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| 5164 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
0.350 |
|
| 5165 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5166 |
\begin{align*}
9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5167 |
\begin{align*}
y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5168 |
\begin{align*}
x +\cos \left (x \right ) y+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5169 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| 5170 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5171 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| 5172 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (1-3 x \right ) y}{\left (x -1\right ) \left (2 x -1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5173 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5174 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5175 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5176 |
\begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5177 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5178 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5179 |
\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. |
✓ |
✓ |
✗ |
✗ |
0.351 |
|
| 5180 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5181 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5182 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5183 |
\begin{align*}
y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| 5184 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| 5185 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5186 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5187 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5188 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=2 x_{3}+3 x_{4} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5189 |
\begin{align*}
y^{\prime }&=3 x +\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5190 |
\begin{align*}
-\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5191 |
\begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5192 |
\begin{align*}
{\mathrm e}^{x} y+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.352 |
|
| 5193 |
\begin{align*}
x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.352 |
|
| 5194 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x^{2}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5195 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5196 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5197 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| 5198 |
\begin{align*}
y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.352 |
|
| 5199 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.352 |
|
| 5200 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.352 |
|