| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 18601 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 18602 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 18603 |
\begin{align*}
y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.320 |
|
| 18604 |
\begin{align*}
x^{\prime \prime }+\left (2+x\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.321 |
|
| 18605 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| 18606 |
\begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.326 |
|
| 18607 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.330 |
|
| 18608 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.335 |
|
| 18609 |
\begin{align*}
y^{\prime }&=\sin \left (t \right ) y+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.335 |
|
| 18610 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.338 |
|
| 18611 |
\begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.341 |
|
| 18612 |
\begin{align*}
y^{\prime }+a y&=k \,{\mathrm e}^{b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| 18613 |
\begin{align*}
2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| 18614 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| 18615 |
\begin{align*}
y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.344 |
|
| 18616 |
\begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.345 |
|
| 18617 |
\begin{align*}
y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.345 |
|
| 18618 |
\begin{align*}
\left (a +x^{2}+y^{2}\right ) y y^{\prime }&=x \left (a -x^{2}-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.348 |
|
| 18619 |
\begin{align*}
\left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.349 |
|
| 18620 |
\begin{align*}
y^{\prime }+3 y&=5 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.349 |
|
| 18621 |
\begin{align*}
y^{\prime } x&=y+x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.351 |
|
| 18622 |
\begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.351 |
|
| 18623 |
\begin{align*}
x^{\prime }&=2 \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.353 |
|
| 18624 |
\begin{align*}
2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.356 |
|
| 18625 |
\begin{align*}
y&=y^{\prime } x +\frac {y {y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.356 |
|
| 18626 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.359 |
|
| 18627 |
\begin{align*}
\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.361 |
|
| 18628 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.362 |
|
| 18629 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
6.362 |
|
| 18630 |
\begin{align*}
y^{\prime }&=-\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a b \,x^{3}}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 b x y^{2}}{2}+\frac {3 a^{2} x^{4} y}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 b^{2} x^{2} y}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 b^{2} x^{4} a}{16}+\frac {b^{3} x^{3}}{8} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.363 |
|
| 18631 |
\begin{align*}
y-y^{\prime } x +x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.363 |
|
| 18632 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.363 |
|
| 18633 |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.365 |
|
| 18634 |
\begin{align*}
x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.365 |
|
| 18635 |
\begin{align*}
y^{\prime \prime }&=f \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.368 |
|
| 18636 |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.369 |
|
| 18637 |
\begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.369 |
|
| 18638 |
\begin{align*}
y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{2 y} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.369 |
|
| 18639 |
\begin{align*}
\left (-a^{2} x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2} \left (-a^{2}+1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.371 |
|
| 18640 |
\begin{align*}
-y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.372 |
|
| 18641 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{x}+{\mathrm e}^{x} \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.372 |
|
| 18642 |
\begin{align*}
y y^{\prime } x&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.375 |
|
| 18643 |
\begin{align*}
-\left (\left (2 n +1\right )^{2}-4 x^{2}\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.376 |
|
| 18644 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.377 |
|
| 18645 |
\begin{align*}
x^{\prime }+2 y^{\prime }-y&=1 \\
2 x^{\prime }+y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.377 |
|
| 18646 |
\begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.379 |
|
| 18647 |
\begin{align*}
y-2 y^{\prime } x&=x {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.379 |
|
| 18648 |
\begin{align*}
1+y+\left (x -y \left (1+y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.380 |
|
| 18649 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.383 |
|
| 18650 |
\begin{align*}
x^{\prime }+4 x-y&=0 \\
x^{\prime }+y^{\prime }&=t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.383 |
|
| 18651 |
\begin{align*}
x +y y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.384 |
|
| 18652 |
\begin{align*}
2 t y+y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.384 |
|
| 18653 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.384 |
|
| 18654 |
\begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.385 |
|
| 18655 |
\begin{align*}
3 x^{\prime }-y&=2 t \\
x^{\prime }+y^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.385 |
|
| 18656 |
\begin{align*}
x^{\prime }+4 y^{\prime }-y&=0 \\
x^{\prime }+2 y&={\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.385 |
|
| 18657 |
\begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.386 |
|
| 18658 |
\begin{align*}
x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.387 |
|
| 18659 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.390 |
|
| 18660 |
\begin{align*}
{\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.391 |
|
| 18661 |
\begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.392 |
|
| 18662 |
\begin{align*}
{y^{\prime }}^{2}&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.395 |
|
| 18663 |
\begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
6.395 |
|
| 18664 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.395 |
|
| 18665 |
\begin{align*}
x^{\prime }+y^{\prime }+x-y&=0 \\
x^{\prime }+2 y^{\prime }+x&=1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.397 |
|
| 18666 |
\begin{align*}
\cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.398 |
|
| 18667 |
\begin{align*}
3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.401 |
|
| 18668 |
\begin{align*}
a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.401 |
|
| 18669 |
\begin{align*}
\left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.401 |
|
| 18670 |
\begin{align*}
y^{\prime }&=-\frac {t}{y} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.402 |
|
| 18671 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\
x_{2}^{\prime }&=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\
x_{3}^{\prime }&=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\
x_{4}^{\prime }&=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\
x_{5}^{\prime }&=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.402 |
|
| 18672 |
\begin{align*}
3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.404 |
|
| 18673 |
\begin{align*}
y+y^{\prime }&=\cos \left (2 t \right ) \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.404 |
|
| 18674 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.404 |
|
| 18675 |
\begin{align*}
x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.405 |
|
| 18676 |
\begin{align*}
r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\
r \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.405 |
|
| 18677 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.405 |
|
| 18678 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.405 |
|
| 18679 |
\begin{align*}
2 x^{\prime }-3 y+y^{\prime }&=0 \\
x^{\prime }+y^{\prime }&=t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.405 |
|
| 18680 |
\begin{align*}
x^{\prime }+2 x-y^{\prime }&=0 \\
x^{\prime }+x+y&=t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.405 |
|
| 18681 |
\begin{align*}
2 x^{2} y^{\prime }+1+2 y x -y^{2} x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.406 |
|
| 18682 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.407 |
|
| 18683 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.407 |
|
| 18684 |
\begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-y x -x^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.408 |
|
| 18685 |
\begin{align*}
y^{\prime }&=3 y+12 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.408 |
|
| 18686 |
\begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.411 |
|
| 18687 |
\begin{align*}
2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.414 |
|
| 18688 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=\sinh \left (x \right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.414 |
|
| 18689 |
\begin{align*}
x^{\prime }+y^{\prime }-x&=\cos \left (t \right ) \\
x^{\prime }+2 y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.417 |
|
| 18690 |
\begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| 18691 |
\begin{align*}
x +y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| 18692 |
\begin{align*}
x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.420 |
|
| 18693 |
\begin{align*}
y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-y x -\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 y^{2} x^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.421 |
|
| 18694 |
\begin{align*}
y+3 y^{\prime } x +2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.421 |
|
| 18695 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.422 |
|
| 18696 |
\begin{align*}
y^{\prime }+a y&=b \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.422 |
|
| 18697 |
\begin{align*}
\left (1+z^{\prime }\right ) {\mathrm e}^{-z}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.423 |
|
| 18698 |
\begin{align*}
x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\
y \left (-4\right ) &= 1 \\
y^{\prime }\left (-4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.424 |
|
| 18699 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.425 |
|
| 18700 |
\begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) x&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.425 |
|