| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10301 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.536 |
|
| 10302 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| 10303 |
\begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| 10304 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| 10305 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2} \\
x_{2}^{\prime }&=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| 10306 |
\begin{align*}
\left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| 10307 |
\begin{align*}
3 y y^{\prime \prime }&=5 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| 10308 |
\begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| 10309 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.537 |
|
| 10310 |
\begin{align*}
y^{\prime }&=f \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| 10311 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| 10312 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| 10313 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10314 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10315 |
\begin{align*}
y^{\prime }&=\frac {1}{1-y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10316 |
\begin{align*}
\frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.538 |
|
| 10317 |
\begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=3 x-2 y \\
z^{\prime }&=-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10318 | \begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.538 |
|
| 10319 |
\begin{align*}
x^{\prime }&=3 x+a y \\
y^{\prime }&=-6 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10320 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
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. |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10321 |
\begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10322 |
\begin{align*}
-x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| 10323 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )+\cos \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10324 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\
x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10325 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10326 |
\begin{align*}
x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10327 |
\begin{align*}
6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10328 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+\left (\frac {1}{4 x^{2}}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10329 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\cos \left (b x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10330 |
\begin{align*}
-2 y x -2 \left (-x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.539 |
|
| 10331 |
\begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10332 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10333 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{k}-b \left (b -1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10334 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-\frac {t}{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10335 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10336 |
\begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 t} \sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10337 | \begin{align*}
y^{\prime \prime }-4 y^{\prime }+2 y&=x \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.539 |
|
| 10338 |
\begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10339 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=6 y+5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10340 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| 10341 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10342 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10343 |
\begin{align*}
y^{\prime \prime } x +\left (4+2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10344 |
\begin{align*}
2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10345 |
\begin{align*}
3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10346 |
\begin{align*}
b +a x y-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (-y^{3}+y^{\prime } y+y^{\prime \prime }\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.540 |
|
| 10347 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10348 |
\begin{align*}
x^{2} y^{\prime \prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| 10349 |
\begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10350 |
\begin{align*}
x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| 10351 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| 10352 |
\begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x+y \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10353 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10354 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| 10355 |
\begin{align*}
y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10356 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| 10357 | \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \left (x +1\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.540 |
|
| 10358 |
\begin{align*}
4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.541 |
|
| 10359 |
\begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| 10360 |
\begin{align*}
y^{\prime \prime }-4 y&=\sin \left (2 x \right ) {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| 10361 |
\begin{align*}
y^{\prime }&=-z \\
z^{\prime }&=y \\
\end{align*} With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| 10362 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| 10363 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| 10364 |
\begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| 10365 |
\begin{align*}
2 y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10366 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10367 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10368 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10369 |
\begin{align*}
y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10370 |
\begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10371 |
\begin{align*}
x \left (y+2\right ) y^{\prime }+a x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10372 |
\begin{align*}
b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.542 |
|
| 10373 |
\begin{align*}
-\left (p^{2}+x^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10374 |
\begin{align*}
-2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10375 |
\begin{align*}
x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.542 |
|
| 10376 | \begin{align*}
y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.542 |
|
| 10377 |
\begin{align*}
12 y-7 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10378 |
\begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10379 |
\begin{align*}
x^{\prime }&=\frac {1}{t^{2}+1} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10380 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-\beta x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10381 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10382 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (2 x \right )+\cos \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10383 |
\begin{align*}
y^{\prime \prime }+16 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| 10384 |
\begin{align*}
2 y^{\prime \prime } x +3 y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10385 |
\begin{align*}
2 y^{\prime \prime } x -y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10386 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=13 x+4 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10387 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10388 |
\begin{align*}
y_{1}^{\prime }&=-3 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10389 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10390 |
\begin{align*}
x^{\prime }-x&=\cos \left (t \right ) \\
y+y^{\prime }&=4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10391 |
\begin{align*}
{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10392 |
\begin{align*}
10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=-1+3 x^{2}+2 \ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.543 |
|
| 10393 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10394 |
\begin{align*}
x^{\prime }&=4 x+5 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10395 | \begin{align*}
x y \left (y^{2}+x^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.543 |
|
| 10396 |
\begin{align*}
\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.543 |
|
| 10397 |
\begin{align*}
a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.543 |
|
| 10398 |
\begin{align*}
10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \\
Q \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10399 |
\begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10400 |
\begin{align*}
y^{\prime }&=\sin \left (x \right )^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|