| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25601 |
\begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
110.378 |
|
| 25602 |
\begin{align*}
c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
110.484 |
|
| 25603 |
\begin{align*}
\left (y^{2}+x^{2}\right ) \left (y^{\prime } x +y\right )&=x y \left (-y+y^{\prime } x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
111.341 |
|
| 25604 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=x y^{\prime } y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
112.069 |
|
| 25605 |
\begin{align*}
y^{\prime } y-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
112.085 |
|
| 25606 |
\begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
112.175 |
|
| 25607 |
\begin{align*}
y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
112.513 |
|
| 25608 |
\begin{align*}
y^{\prime } y-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
112.685 |
|
| 25609 |
\begin{align*}
y^{\prime } y-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y&=n \left (x -a \right ) x^{-2 n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
113.552 |
|
| 25610 |
\begin{align*}
y^{\prime }&=t^{m} y^{n} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
113.811 |
|
| 25611 |
\begin{align*}
\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
114.637 |
|
| 25612 |
\begin{align*}
x^{2} \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) x y^{\prime }+d y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
116.277 |
|
| 25613 |
\begin{align*}
2 \left (1-b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
117.124 |
|
| 25614 |
\begin{align*}
n \left (a +n \right ) y+\left (c -\left (a +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
118.099 |
|
| 25615 |
\begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+\left (2+\frac {5 \,{\mathrm e}^{x}}{2}\right ) y+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
118.375 |
|
| 25616 |
\begin{align*}
y^{\prime } y-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
118.556 |
|
| 25617 |
\begin{align*}
y^{\prime }&=\frac {y}{x}-\csc \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
118.658 |
|
| 25618 | \begin{align*}
x \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) y^{\prime }+s x y&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 120.214 |
|
| 25619 |
\begin{align*}
\left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
121.221 |
|
| 25620 |
\begin{align*}
c x y+\left (a -\left (a +1\right ) x^{2}\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
122.010 |
|
| 25621 |
\begin{align*}
{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
122.499 |
|
| 25622 |
\begin{align*}
2 x -y+1+\left (x -2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
123.100 |
|
| 25623 |
\begin{align*}
y \sqrt {x^{2}-1}+x \sqrt {y^{2}-1}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
123.590 |
|
| 25624 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (3 x^{2}-1\right ) y^{\prime }}{\left (x^{2}-1\right ) x}-\frac {\left (x^{2}-1-\left (2 v +1\right )^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
123.629 |
|
| 25625 |
\begin{align*}
y^{\prime }&=-\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
123.855 |
|
| 25626 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \left (y^{\prime } y+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
123.985 |
|
| 25627 |
\begin{align*}
y^{\prime } y&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
124.284 |
|
| 25628 |
\begin{align*}
y^{\prime }&=\frac {2 x \ln \left (\frac {1}{x -1}\right )-\coth \left (\frac {x +1}{x -1}\right )+\coth \left (\frac {x +1}{x -1}\right ) y^{2}-2 \coth \left (\frac {x +1}{x -1}\right ) x^{2} y+\coth \left (\frac {x +1}{x -1}\right ) x^{4}}{\ln \left (\frac {1}{x -1}\right )} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
124.306 |
|
| 25629 |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
124.488 |
|
| 25630 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \,x^{n}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
124.744 |
|
| 25631 |
\begin{align*}
c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
125.175 |
|
| 25632 |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
125.212 |
|
| 25633 |
\begin{align*}
\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
125.619 |
|
| 25634 |
\begin{align*}
\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
125.749 |
|
| 25635 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
126.199 |
|
| 25636 |
\begin{align*}
x^{2} y^{\prime }&=y^{2} a^{2} x^{2}-y x +b^{2} \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
127.203 |
|
| 25637 |
\begin{align*}
y^{\prime } y-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
128.471 |
|
| 25638 | \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 128.487 |
|
| 25639 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
128.510 |
|
| 25640 |
\begin{align*}
y^{\prime } y-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
128.576 |
|
| 25641 |
\begin{align*}
y^{\prime \prime }&=\frac {2 x \left (2 a -1\right ) y^{\prime }}{x^{2}-1}-\frac {\left (x^{2} \left (2 a \left (2 a -1\right )-v \left (v +1\right )\right )+2 a +v \left (v +1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
129.267 |
|
| 25642 |
\begin{align*}
\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime \prime }+\left (b_{1} x +c_{1} \right ) y^{\prime }+c_{0} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
129.420 |
|
| 25643 |
\begin{align*}
y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
129.444 |
|
| 25644 |
\begin{align*}
x^{2} \left (x +a_{2} \right ) y^{\prime \prime }+x \left (b_{1} x +a_{1} \right ) y^{\prime }+\left (b_{0} x +a_{0} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
129.488 |
|
| 25645 |
\begin{align*}
y^{\prime }&=-\frac {2+x}{x \left (x +1\right )^{2}}-\frac {\left (-x^{2}+x +2\right ) y}{x \left (x +1\right )}+\left (x +1\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
130.049 |
|
| 25646 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
130.405 |
|
| 25647 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\alpha -\beta +\left (\alpha +\beta -2\right ) x \right ) y^{\prime }+\left (n +1\right ) \left (n +\alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
130.622 |
|
| 25648 |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
131.004 |
|
| 25649 |
\begin{align*}
x y \left (1-{y^{\prime }}^{2}\right )&=\left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
131.060 |
|
| 25650 |
\begin{align*}
y^{\prime } y-y&=A x +B \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
131.145 |
|
| 25651 |
\begin{align*}
n \left (1+a +b +n \right ) y+\left (-a +b -\left (2+a +b \right ) x \right ) y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
131.240 |
|
| 25652 |
\begin{align*}
y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
131.329 |
|
| 25653 |
\begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (20 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
131.373 |
|
| 25654 |
\begin{align*}
\sin \left (y\right )^{3} y^{\prime \prime }&=\cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
131.672 |
|
| 25655 |
\begin{align*}
4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
132.618 |
|
| 25656 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
132.700 |
|
| 25657 | \begin{align*}
y^{\prime }&=\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 132.826 |
|
| 25658 |
\begin{align*}
y&=2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
133.033 |
|
| 25659 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
133.328 |
|
| 25660 |
\begin{align*}
y^{\prime } x&=\lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
133.343 |
|
| 25661 |
\begin{align*}
\left (a \cot \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \cot \left (\mu x \right ) y-d^{2}+c d \cot \left (\mu x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
133.615 |
|
| 25662 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
134.348 |
|
| 25663 |
\begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
134.660 |
|
| 25664 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
x_{3}^{\prime }&=6 x_{1}-6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
135.430 |
|
| 25665 |
\begin{align*}
y^{\prime } y-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
136.128 |
|
| 25666 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
136.314 |
|
| 25667 |
\begin{align*}
\operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x \left (x^{2}+\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
136.758 |
|
| 25668 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }-\left (-k^{2}+x^{2}\right ) y^{\prime }+\left (k +x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
136.796 |
|
| 25669 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\beta -\alpha -\left (\alpha +\beta +2\right ) x \right ) y^{\prime }+n \left (n +\alpha +\beta +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
137.399 |
|
| 25670 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \,x^{2}+a -2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {b y}{x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
137.477 |
|
| 25671 |
\begin{align*}
x^{3} y^{\prime }&=a \,x^{3} y^{2}+x \left (b x +c \right ) y+x \alpha +\beta \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
137.804 |
|
| 25672 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x -\gamma \right ) y^{\prime }+\alpha \beta y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
138.553 |
|
| 25673 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (a \,x^{2}+a -1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (b \,x^{2}+c \right ) y}{x^{2} \left (x^{2}+1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
138.705 |
|
| 25674 |
\begin{align*}
x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3}&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
138.777 |
|
| 25675 |
\begin{align*}
b^{2} y+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
139.627 |
|
| 25676 |
\begin{align*}
x^{2} y^{\prime }&=x^{4} y^{2}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
139.690 |
|
| 25677 | \begin{align*}
y^{\prime } y-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} | ✗ | ✗ | ✗ | ✗ | 139.810 |
|
| 25678 |
\begin{align*}
y^{\prime }&=a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
140.188 |
|
| 25679 |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (\lambda \left (a +c \right ) x^{2}+\left (c -a \right ) x +2 b \lambda \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
140.421 |
|
| 25680 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 a x +b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (a v x -b \right ) y}{\left (a x +b \right ) x^{2}}+A x \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
140.835 |
|
| 25681 |
\begin{align*}
y^{\prime \prime }&=\frac {2 y^{\prime }}{x \left (x -2\right )}-\frac {y}{x^{2} \left (x -2\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
141.892 |
|
| 25682 |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
142.140 |
|
| 25683 |
\begin{align*}
y^{\prime } y-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y&=-\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
143.492 |
|
| 25684 |
\begin{align*}
x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
143.958 |
|
| 25685 |
\begin{align*}
\left (y-3 x +3\right ) y^{\prime }&=2 y-x -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
145.332 |
|
| 25686 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \left (y^{\prime } y+x \right )&=a^{2} y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
145.536 |
|
| 25687 |
\begin{align*}
2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
145.591 |
|
| 25688 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\left (a +b +1\right ) x +\alpha +\beta -1\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (a b x -\alpha \beta \right ) y}{x^{2} \left (x -1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
145.611 |
|
| 25689 |
\begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
147.220 |
|
| 25690 |
\begin{align*}
-y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=\left (x +1\right ) \sec \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
147.852 |
|
| 25691 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
147.855 |
|
| 25692 |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
148.439 |
|
| 25693 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
148.598 |
|
| 25694 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-k x +x^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
149.687 |
|
| 25695 |
\begin{align*}
y&=-a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
150.202 |
|
| 25696 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 \left (n +1\right ) x^{2}+2 n +1\right ) y^{\prime }-\left (v -n \right ) \left (v +n +1\right ) x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
151.565 |
|
| 25697 | \begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }-\left (2 \left (n -1\right ) x^{2}+2 n -1\right ) y^{\prime }+\left (v +n \right ) \left (-v +n -1\right ) x y&=0 \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 151.863 |
|
| 25698 |
\begin{align*}
\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +f \right ) y^{\prime }+g y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
153.312 |
|
| 25699 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
153.741 |
|
| 25700 |
\begin{align*}
-x^{\prime \prime }&=1-x-x^{2} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
153.901 |
|