| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 17401 |
\begin{align*}
y^{\prime }&=y \left (t +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| 17402 |
\begin{align*}
-8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=4 x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.797 |
|
| 17403 |
\begin{align*}
x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\
x \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.797 |
|
| 17404 |
\begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.797 |
|
| 17405 |
\begin{align*}
y^{\prime }+3 y&=1 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.798 |
|
| 17406 |
\begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.798 |
|
| 17407 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.798 |
|
| 17408 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.799 |
|
| 17409 |
\begin{align*}
y^{\prime }&=\frac {1}{t^{2}+1}-y \\
y \left (2\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| 17410 |
\begin{align*}
4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.800 |
|
| 17411 |
\begin{align*}
x \left (x -1\right ) y^{\prime }+y&=x^{2} \left (2 x -1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| 17412 |
\begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.801 |
|
| 17413 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.801 |
|
| 17414 |
\begin{align*}
x y^{\prime \prime }+y \sin \left (x \right )&=x \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*}
Series expansion around \(x=\pi \). |
✓ |
✓ |
✓ |
✗ |
2.801 |
|
| 17415 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| 17416 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| 17417 |
\begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| 17418 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| 17419 |
\begin{align*}
2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.802 |
|
| 17420 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| 17421 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.802 |
|
| 17422 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| 17423 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.803 |
|
| 17424 |
\begin{align*}
2 x y y^{\prime \prime }&=-y y^{\prime }+{y^{\prime }}^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.803 |
|
| 17425 |
\begin{align*}
y^{\prime }&=2 y+{\mathrm e}^{t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| 17426 |
\begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| 17427 |
\begin{align*}
2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.805 |
|
| 17428 |
\begin{align*}
y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| 17429 |
\begin{align*}
L i^{\prime }+R i&=e \sin \left (w t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| 17430 |
\begin{align*}
y^{\prime }-a \left (t \right ) y&={\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| 17431 |
\begin{align*}
4 x y^{\prime \prime }-\left (x +a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.807 |
|
| 17432 |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| 17433 |
\begin{align*}
y-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| 17434 |
\begin{align*}
y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.808 |
|
| 17435 |
\begin{align*}
x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\
x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\
x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 17436 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 17437 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=12 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 17438 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=18 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 17439 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 17440 |
\begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| 17441 |
\begin{align*}
\ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.810 |
|
| 17442 |
\begin{align*}
\left (y^{2}-1\right ) y^{\prime }&=4 y x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.810 |
|
| 17443 |
\begin{align*}
{y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.811 |
|
| 17444 |
\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. |
✓ |
✓ |
✓ |
✓ |
2.811 |
|
| 17445 |
\begin{align*}
x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.812 |
|
| 17446 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.813 |
|
| 17447 |
\begin{align*}
-a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.813 |
|
| 17448 |
\begin{align*}
-2 b y+2 a y^{\prime }+x \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.814 |
|
| 17449 |
\begin{align*}
x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.816 |
|
| 17450 |
\begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.818 |
|
| 17451 |
\begin{align*}
-y+x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.819 |
|
| 17452 |
\begin{align*}
y^{\prime }-y x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.819 |
|
| 17453 |
\begin{align*}
-y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.819 |
|
| 17454 |
\begin{align*}
y^{\prime }+\frac {y}{-3+t}&=\frac {1}{t -1} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| 17455 |
\begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| 17456 |
\begin{align*}
x y^{\prime }+6 y&=1+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| 17457 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.822 |
|
| 17458 |
\begin{align*}
t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.822 |
|
| 17459 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.822 |
|
| 17460 |
\begin{align*}
x^{\prime }+5 x&=\operatorname {Heaviside}\left (t -2\right ) \\
x \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| 17461 |
\begin{align*}
y^{\prime \prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| 17462 |
\begin{align*}
y^{\prime \prime }&=-a^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| 17463 |
\begin{align*}
y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.824 |
|
| 17464 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{r}&=4-4 r \\
u \left (1\right ) &= 15 \\
u^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.824 |
|
| 17465 |
\begin{align*}
y^{\prime }+2 y x&=2 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.825 |
|
| 17466 |
\begin{align*}
x y^{\prime }&=a \,x^{m}-b y-c \,x^{n} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.826 |
|
| 17467 |
\begin{align*}
x^{\prime }&=-x t \\
x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.826 |
|
| 17468 |
\begin{align*}
\left (x +{\mathrm e}^{y}\right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| 17469 |
\begin{align*}
-5 y-3 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| 17470 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.828 |
|
| 17471 |
\begin{align*}
x y^{\prime }-y&=x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| 17472 |
\begin{align*}
y^{\prime }+y&=x^{2}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| 17473 |
\begin{align*}
y^{\prime }&=\left (y+\frac {1}{2}\right ) \left (t +y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.829 |
|
| 17474 |
\begin{align*}
\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.830 |
|
| 17475 |
\begin{align*}
4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.831 |
|
| 17476 |
\begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+y+x^{2} y^{3}+x^{3} y^{4}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| 17477 |
\begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.832 |
|
| 17478 |
\begin{align*}
6 y-4 \left (x +a \right ) y^{\prime }+\left (x +a \right )^{2} y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| 17479 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.834 |
|
| 17480 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.834 |
|
| 17481 |
\begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| 17482 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| 17483 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| 17484 |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| 17485 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.836 |
|
| 17486 |
\begin{align*}
2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.836 |
|
| 17487 |
\begin{align*}
r^{\prime }&=\frac {r^{2}}{x} \\
r \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| 17488 |
\begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| 17489 |
\begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.838 |
|
| 17490 |
\begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.838 |
|
| 17491 |
\begin{align*}
y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.838 |
|
| 17492 |
\begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 17493 |
\begin{align*}
y^{\prime \prime }+w^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 17494 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 17495 |
\begin{align*}
y^{\prime }&=x +\sin \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| 17496 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.840 |
|
| 17497 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| 17498 |
\begin{align*}
x^{\prime }-x t&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| 17499 |
\begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.843 |
|
| 17500 |
\begin{align*}
2 x +2 x y^{2}-y^{3}-y^{5}+\left (1-3 x y^{2}-3 x y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.843 |
|