| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10301 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10302 |
\begin{align*}
y&=y^{\prime } \left (-b +x \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.714 |
|
| 10303 |
\begin{align*}
y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10304 |
\begin{align*}
x^{\prime }&=\left (a -2\right ) x+y \\
y^{\prime }&=-x+\left (a -2\right ) y \\
z^{\prime }&=-a z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| 10305 |
\begin{align*}
9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10306 |
\begin{align*}
x^{\prime }+2 x&=3 t \\
x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10307 |
\begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.715 |
|
| 10308 |
\begin{align*}
x^{\prime }&=x-3 y \\
y^{\prime }&=3 x+7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10309 |
\begin{align*}
y^{\prime \prime }+4 y&=-3 t^{2}+2 t +3 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10310 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} \arctan \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10311 |
\begin{align*}
y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10312 |
\begin{align*}
3 x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10313 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -1\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| 10314 |
\begin{align*}
3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| 10315 |
\begin{align*}
t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(t=1\). |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| 10316 |
\begin{align*}
y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| 10317 |
\begin{align*}
y&=x^{6} {y^{\prime }}^{3}-y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.716 |
|
| 10318 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| 10319 |
\begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {y}{x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| 10320 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\tan \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| 10321 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2} \\
x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\
x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 5 \\
x_{3} \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| 10322 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| 10323 |
\begin{align*}
x^{\prime }&=x+3 y+2 t \\
y^{\prime }&=x-y+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| 10324 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y \ln \left (x \right )&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10325 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10326 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.718 |
|
| 10327 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-4 x_{2} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10328 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.718 |
|
| 10329 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10330 |
\begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z \\
z^{\prime }&=z-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10331 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10332 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.718 |
|
| 10333 |
\begin{align*}
y^{\prime \prime }+a^{2} y-2 a y^{\prime }+b^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| 10334 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10335 |
\begin{align*}
{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10336 |
\begin{align*}
\left (2 x +y+1\right ) y-x \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.719 |
|
| 10337 |
\begin{align*}
y^{\prime \prime \prime }&=x^{2}+{\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10338 |
\begin{align*}
x^{\prime }&=6 x-y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10339 |
\begin{align*}
2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10340 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10341 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.719 |
|
| 10342 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+4 x&={\mathrm e}^{t} \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10343 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.719 |
|
| 10344 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10345 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10346 |
\begin{align*}
t^{2} \left (1+t \right ) y^{\prime \prime }-t \left (2 t +1\right ) y^{\prime }+\left (2 t +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| 10347 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10348 |
\begin{align*}
25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10349 |
\begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10350 |
\begin{align*}
2 y x -\left (-x^{2}+4\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| 10351 |
\begin{align*}
2 a^{2} y-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10352 |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10353 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10354 |
\begin{align*}
y^{\prime }+y \ln \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| 10355 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10356 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10357 |
\begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10358 |
\begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| 10359 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+\left (-x^{2}+1\right ) y&=\frac {-x^{2}+x}{x +1} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| 10360 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10361 |
\begin{align*}
y^{\prime \prime } x +x&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10362 |
\begin{align*}
y \cos \left (y x \right )-\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.721 |
|
| 10363 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10364 |
\begin{align*}
y^{\prime }-y^{2}-3 y+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10365 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=2-6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10366 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10367 |
\begin{align*}
x^{\prime \prime }+2 b x^{\prime }+k^{2} x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= v_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| 10368 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 10369 |
\begin{align*}
x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\
x \left (0\right ) &= {\frac {1}{10}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 10370 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 10371 |
\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.722 |
|
| 10372 |
\begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=y+3 z \\
z^{\prime }&=3 y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 10373 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| 10374 |
\begin{align*}
x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10375 |
\begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10376 |
\begin{align*}
\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10377 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&={\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| 10378 |
\begin{align*}
-\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| 10379 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10380 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10381 |
\begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| 10382 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10383 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| 10384 |
\begin{align*}
y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| 10385 |
\begin{align*}
t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| 10386 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\frac {1}{\left (x^{2}+1\right ) y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 10387 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.724 |
|
| 10388 |
\begin{align*}
x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 \left (1-6 x \right ) x y^{\prime }+\left (1-12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 10389 |
\begin{align*}
x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| 10390 |
\begin{align*}
-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
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| 10391 |
\begin{align*}
y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{a \,x^{2}+b x +c}}&=0 \\
\end{align*} |
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| 10392 |
\begin{align*}
y^{\prime }&=\frac {2 x y^{2}+4 y \ln \left (2 x +1\right ) x +2 \ln \left (2 x +1\right )^{2} x +y^{2}-2+\ln \left (2 x +1\right )^{2}+2 y \ln \left (2 x +1\right )}{2 x +1} \\
\end{align*} |
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| 10393 |
\begin{align*}
x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
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| 10394 |
\begin{align*}
v^{\prime }&=\frac {K -v}{R C} \\
\end{align*} |
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| 10395 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-4 y \\
z^{\prime }&=-z \\
\end{align*} |
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| 10396 |
\begin{align*}
u^{\prime \prime }+w_{0}^{2} u&=\cos \left (w t \right ) \\
\end{align*} |
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| 10397 |
\begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
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| 10398 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
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| 10399 |
\begin{align*}
x^{\prime }&=2 x-y+{\mathrm e}^{t} \\
y^{\prime }&=3 x-2 y+t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
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| 10400 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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