| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9201 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9202 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9203 |
\begin{align*}
y^{\prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9204 |
\begin{align*}
x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 9205 |
\begin{align*}
y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9206 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9207 |
\begin{align*}
y^{\prime \prime }+y \ln \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9208 |
\begin{align*}
2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\
x \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9209 |
\begin{align*}
y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9210 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9211 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=\frac {6}{1+{\mathrm e}^{-2 x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 9212 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=\sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9213 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9214 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9215 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9216 |
\begin{align*}
y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| 9217 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9218 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9219 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9220 |
\begin{align*}
x^{\prime }+4 x+3 y&=t \\
y^{\prime }+2 x+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9221 |
\begin{align*}
x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9222 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9223 |
\begin{align*}
x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9224 |
\begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
y^{\prime \prime }\left (0\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9225 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9226 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9227 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-\left (1+3 x \right ) y^{\prime }-\left (x^{2}-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.680 |
|
| 9228 |
\begin{align*}
x^{\prime \prime }&=-\frac {x}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9229 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9230 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9231 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| 9232 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9233 |
\begin{align*}
x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 9234 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-3 y x&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9235 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9236 |
\begin{align*}
16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9237 |
\begin{align*}
2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9238 |
\begin{align*}
\left (-x y^{\prime }+y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 9239 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9240 |
\begin{align*}
{\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9241 |
\begin{align*}
y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9242 |
\begin{align*}
p \left (1+p \right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9243 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9244 |
\begin{align*}
y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9245 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9246 |
\begin{align*}
x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 9247 |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9248 |
\begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9249 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9250 |
\begin{align*}
{y^{\prime }}^{2}+4 x y^{\prime }-y^{2}-2 x^{2} y&=x^{4}-4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| 9251 |
\begin{align*}
5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| 9252 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}+{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9253 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9254 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9255 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9256 |
\begin{align*}
x \left (y x +1\right ) y^{\prime \prime }+{y^{\prime }}^{2} x^{2}+\left (4 y x +2\right ) y^{\prime }+y^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.682 |
|
| 9257 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9258 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9259 |
\begin{align*}
y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\sin \left (n x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| 9260 |
\begin{align*}
y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9261 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9262 |
\begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-2 x+5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9263 |
\begin{align*}
y^{\prime }&=1+\frac {\sec \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9264 |
\begin{align*}
y^{\prime \prime }+y-a \cos \left (b x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9265 |
\begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=3 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9266 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| 9267 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\
x \left (0\right ) &= 10 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9268 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9269 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{3} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9270 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9271 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9272 |
\begin{align*}
y^{\prime \prime }+4 y&=t \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= \frac {\pi }{16} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9273 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9274 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9275 |
\begin{align*}
y^{\prime \prime }-11 y^{\prime }+30 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9276 |
\begin{align*}
y^{\prime \prime }+y&=-2 x +2 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9277 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9278 |
\begin{align*}
x_{1}^{\prime }&=a x_{1} \\
x_{2}^{\prime }&=a x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+a x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9279 |
\begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9280 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9281 |
\begin{align*}
y^{\prime \prime }-y&=\frac {1}{\left (1-{\mathrm e}^{2 x}\right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| 9282 |
\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 0 & 1-i \\ 0 & -1-i & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.684 |
|
| 9283 |
\begin{align*}
y^{\prime }+y^{\prime \prime \prime }&=\sin \left (x \right )+x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9284 |
\begin{align*}
2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.685 |
|
| 9285 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.685 |
|
| 9286 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=50 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9287 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 x+2 y-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9288 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} x \\
y \left (2\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9289 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9290 |
\begin{align*}
y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9291 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9292 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9293 |
\begin{align*}
x y^{\prime \prime }+{y^{\prime }}^{2} x -y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| 9294 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left (1+{\mathrm e}^{x}\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.685 |
|
| 9295 |
\begin{align*}
y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.685 |
|
| 9296 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 9297 |
\begin{align*}
y y^{\prime \prime }-y^{2} y^{\prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.686 |
|
| 9298 |
\begin{align*}
x y^{\prime \prime }-{y^{\prime }}^{2} x^{2}+2 y^{\prime }+y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.686 |
|
| 9299 |
\begin{align*}
x^{\prime }+3 x-y&={\mathrm e}^{2 t} \\
y^{\prime }+x+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| 9300 |
\begin{align*}
y^{\prime \prime }-k^{2} y&=f \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.686 |
|