| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10201 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10202 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10203 |
\begin{align*}
x^{\prime }&=z \\
y^{\prime }&=-z \\
z^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10204 |
\begin{align*}
\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.779 |
|
| 10205 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10206 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10207 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 10208 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -20 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 10209 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.780 |
|
| 10210 |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 10211 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=-2 t \\
x^{\prime }+y^{\prime }+x-y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 10212 |
\begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 10213 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 10214 |
\begin{align*}
x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.780 |
|
| 10215 |
\begin{align*}
y^{\prime }+y-x^{\prime }+x&=t \\
x^{\prime }+y^{\prime }+x-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 10216 |
\begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\
x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10217 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10218 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \cos \left (2 x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10219 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10220 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10221 |
\begin{align*}
x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10222 |
\begin{align*}
x^{2} y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}-b \,x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.781 |
|
| 10223 |
\begin{align*}
2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.781 |
|
| 10224 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10225 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10226 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10227 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=2 y+z \\
z^{\prime }&=x+3 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 10228 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=\frac {6}{1+{\mathrm e}^{-2 x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.781 |
|
| 10229 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10230 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10231 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10232 |
\begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10233 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10234 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10235 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=8 \sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 10236 |
\begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10237 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10238 |
\begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10239 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10240 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10241 |
\begin{align*}
y^{\prime }&=x -\frac {1}{3} x^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10242 |
\begin{align*}
y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10243 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10244 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10245 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10246 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10247 |
\begin{align*}
y^{\prime \prime }+2&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10248 |
\begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\
\end{align*} Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
0.783 |
|
| 10249 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 10250 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 10251 |
\begin{align*}
y_{1}^{\prime }&=-2 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}-2 y_{2}-y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 10252 |
\begin{align*}
x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.784 |
|
| 10253 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| 10254 |
\begin{align*}
a \cos \left (x \right ) y-\sin \left (x \right ) y^{2}+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.785 |
|
| 10255 |
\begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.785 |
|
| 10256 |
\begin{align*}
y^{\prime } x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10257 |
\begin{align*}
-y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.785 |
|
| 10258 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10259 |
\begin{align*}
y^{\prime \prime }+y&=3 \cos \left (w t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10260 |
\begin{align*}
x^{\prime }+2 y^{\prime }-2 x+2 y&=3 \,{\mathrm e}^{t} \\
3 x^{\prime }+y^{\prime }+2 x+y&=4 \,{\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10261 |
\begin{align*}
y^{\prime }+2 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10262 |
\begin{align*}
x^{\prime }-x-2 y&=0 \\
y^{\prime }-2 y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10263 |
\begin{align*}
y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| 10264 |
\begin{align*}
y^{\prime }&=y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10265 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10266 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10267 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10268 |
\begin{align*}
y^{\prime \prime }+4 y&=\tan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10269 |
\begin{align*}
x^{\prime }&=2 x+4 y+\cos \left (t \right ) \\
y^{\prime }&=-x-2 y+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10270 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10271 |
\begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10272 |
\begin{align*}
x^{\prime }&=3 x+2 y+2 z \\
y^{\prime }&=x+4 y+z \\
z^{\prime }&=-2 x-4 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10273 |
\begin{align*}
x^{\prime }&=-10 x+y+7 z \\
y^{\prime }&=-9 x+4 y+5 z \\
z^{\prime }&=-17 x+y+12 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10274 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=8 \sin \left (t \right ) \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10275 |
\begin{align*}
y^{\prime \prime }-y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10276 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| 10277 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| 10278 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10279 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10280 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10281 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }&=\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.787 |
|
| 10282 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10283 |
\begin{align*}
y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10284 |
\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.787 |
|
| 10285 |
\begin{align*}
x^{\prime }&=1+x \\
y^{\prime }&=x+3 y-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| 10286 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+x +1\right ) y^{\prime }+x \left (2-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10287 |
\begin{align*}
x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| 10288 |
\begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-x_{3} \\
\end{align*} |
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0.788 |
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| 10289 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.788 |
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| 10290 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= -6 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} Series expansion around \(x=1\). |
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0.788 |
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| 10291 |
\begin{align*}
a y^{\prime \prime }&=0 \\
\end{align*} |
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0.788 |
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| 10292 |
\begin{align*}
x^{\prime }&=4 x \\
y^{\prime }&=x-2 y \\
z^{\prime }&=x-4 y+z \\
\end{align*} |
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0.788 |
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| 10293 |
\begin{align*}
\left (2 y^{\prime } x -y\right )^{2}&=8 x^{3} \\
\end{align*} |
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0.788 |
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| 10294 |
\begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \sin \left (2 x \right ) \\
\end{align*} |
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0.788 |
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| 10295 |
\begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
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0.788 |
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| 10296 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} |
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0.788 |
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| 10297 |
\begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
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0.789 |
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| 10298 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )+\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
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0.789 |
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| 10299 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y p&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.789 |
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| 10300 |
\begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
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0.789 |
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