| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10201 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10202 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10203 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.766 |
|
| 10204 |
\begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10205 |
\begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10206 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10207 |
\begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10208 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10209 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=-x_{1}-3 x_{2}+2 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10210 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10211 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{3 x} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10212 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.767 |
|
| 10213 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10214 |
\begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10215 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10216 |
\begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{2}-y_{2}+5 \\
y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{2}-5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10217 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10218 |
\begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.768 |
|
| 10219 |
\begin{align*}
x^{\prime }&=-2 x+y+t \\
y^{\prime }&=-4 x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10220 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.768 |
|
| 10221 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10222 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=x^{3}+x +{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10223 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )-\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10224 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10225 |
\begin{align*}
2 y^{\prime \prime }+4 y&={\mathrm e}^{i t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10226 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\
x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10227 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10228 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10229 |
\begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10230 |
\begin{align*}
x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| 10231 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=3 t^{3}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10232 |
\begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10233 |
\begin{align*}
y^{\prime \prime }+3 y&=5 \delta \left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10234 |
\begin{align*}
y^{\prime }-y^{3}&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10235 |
\begin{align*}
x y^{\prime \prime }+\left (1-{\mathrm e}^{x}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10236 |
\begin{align*}
\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10237 |
\begin{align*}
t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime }&=1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.769 |
|
| 10238 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10239 |
\begin{align*}
y^{\prime }-x y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10240 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10241 |
\begin{align*}
y^{\prime \prime }+y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10242 |
\begin{align*}
y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10243 |
\begin{align*}
x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| 10244 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| 10245 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10246 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10247 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=-x_{1} \\
x_{3}^{\prime }&=5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10248 |
\begin{align*}
x y^{2} y^{\prime \prime }&=a \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.770 |
|
| 10249 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10250 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10251 |
\begin{align*}
x^{\prime }&=3 y \\
y^{\prime }&=3 \pi y-\frac {x}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10252 |
\begin{align*}
y y^{\prime \prime }&=-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10253 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10254 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x} \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10255 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10256 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10257 |
\begin{align*}
y^{\prime \prime }-2 y x&=x^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| 10258 |
\begin{align*}
y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10259 |
\begin{align*}
r^{\prime \prime }+2 r^{\prime }+r&=1 \\
r \left (0\right ) &= 0 \\
r^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| 10260 |
\begin{align*}
-\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.771 |
|
| 10261 |
\begin{align*}
a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.771 |
|
| 10262 |
\begin{align*}
4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10263 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=4 t +5 \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10264 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=8 x-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (1\right ) &= 2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10265 |
\begin{align*}
s^{\prime \prime }&=5 t^{2}-7 t \\
s \left (0\right ) &= 0 \\
s \left (1\right ) &= {\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10266 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=f \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. |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10267 |
\begin{align*}
x&={y^{\prime }}^{3}+y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| 10268 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1} \\
x_{2}^{\prime }&=x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10269 |
\begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| 10270 |
\begin{align*}
2 x y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| 10271 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x +1 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.772 |
|
| 10272 |
\begin{align*}
9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10273 |
\begin{align*}
x_{1}^{\prime }&=-8 x_{1}+6 x_{2}-3 x_{3} \\
x_{2}^{\prime }&=-12 x_{1}+10 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=-2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10274 |
\begin{align*}
2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10275 |
\begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10276 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10277 |
\begin{align*}
x y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 10278 |
\begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10279 |
\begin{align*}
-4 y-3 y^{\prime }+y^{\prime \prime }&=16 x -12 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10280 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10281 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10282 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10283 |
\begin{align*}
y^{\prime \prime }+9 y&=36 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10284 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10285 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10286 |
\begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 10287 |
\begin{align*}
x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10288 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10289 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2} \\
y_{2}^{\prime }&=2 y_{1}+3 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10290 |
\begin{align*}
\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10291 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (0\right ) &= {\frac {33}{40}} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10292 |
\begin{align*}
x^{\prime }&=x-5 y \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10293 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10294 |
\begin{align*}
y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.774 |
|
| 10295 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10296 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10297 |
\begin{align*}
{y^{\prime }}^{2} x +\left (k -x -y\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.774 |
|
| 10298 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=2 t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.774 |
|
| 10299 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2}+{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 10300 |
\begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=3 x+z \\
z^{\prime }&=3 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|