| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y y^{\prime }-y&=\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
52.861 |
|
| \begin{align*}
y y^{\prime }-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
55.694 |
|
| \begin{align*}
y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
66.385 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
142.803 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
79.763 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
90.083 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
126.910 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {A}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
129.450 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
193.089 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
124.206 |
|
| \begin{align*}
y y^{\prime }-y&=2 x +\frac {A}{x^{2}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
23.254 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
175.009 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
128.810 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
136.084 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
200.927 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
199.850 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
112.157 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
178.807 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
202.928 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
124.016 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
193.842 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
119.490 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {A}{x^{2}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
18.047 |
|
| \begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
292.074 |
|
| \begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
236.406 |
|
| \begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
167.948 |
|
| \begin{align*}
y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
124.417 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
179.365 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
193.366 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
132.089 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
175.861 |
|
| \begin{align*}
y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
88.698 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
95.212 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
95.165 |
|
| \begin{align*}
y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
✗ |
63.608 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
138.228 |
|
| \begin{align*}
y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
206.063 |
|
| \begin{align*}
y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
208.263 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
242.517 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
138.699 |
|
| \begin{align*}
y y^{\prime }-y&=6 x +\frac {A}{x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
30.657 |
|
| \begin{align*}
y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
127.634 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {A}{x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
✗ |
45.756 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
223.219 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
245.751 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
218.039 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
150.082 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
210.667 |
|
| \begin{align*}
y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
187.439 |
|
| \begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
441.402 |
|
| \begin{align*}
y y^{\prime }-y&=a x +b \,x^{m} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
154.829 |
|
| \begin{align*}
y y^{\prime }-y&=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
121.970 |
|
| \begin{align*}
y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
61.809 |
|
| \begin{align*}
y y^{\prime }&=\left (a x +b \right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
130.379 |
|
| \begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
96.091 |
|
| \begin{align*}
y y^{\prime }&=\left (a -\frac {1}{a x}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
154.925 |
|
| \begin{align*}
y y^{\prime }&=\frac {y}{\sqrt {a x +b}}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
88.628 |
|
| \begin{align*}
y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
186.312 |
|
| \begin{align*}
y y^{\prime }&=\left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
143.617 |
|
| \begin{align*}
y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
63.072 |
|
| \begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
94.205 |
|
| \begin{align*}
y y^{\prime }&=a y \cosh \left (x \right )+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
93.173 |
|
| \begin{align*}
y y^{\prime }&=a \cos \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
72.616 |
|
| \begin{align*}
y y^{\prime }&=a \sin \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
165.049 |
|
| \begin{align*}
y y^{\prime }&=\left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
159.635 |
|
| \begin{align*}
y y^{\prime }&=\left (3 a x +b \right ) y-a^{2} x^{3}-a b \,x^{2}+c x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
61.927 |
|
| \begin{align*}
2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
142.329 |
|
| \begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
239.288 |
|
| \begin{align*}
y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
228.819 |
|
| \begin{align*}
y y^{\prime }+a \left (1-\frac {1}{x}\right ) y&=a^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
177.737 |
|
| \begin{align*}
y y^{\prime }-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
185.558 |
|
| \begin{align*}
y y^{\prime }&=x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (a +x \right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✗ |
✗ |
256.303 |
|
| \begin{align*}
y y^{\prime }&=a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
384.433 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (x \left (m -1\right )+1\right ) y}{x}&=\frac {a^{2} \left (x m +1\right ) \left (-1+x \right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
127.766 |
|
| \begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
219.747 |
|
| \begin{align*}
y y^{\prime }&=\frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
60.866 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (-1+x \right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
183.500 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
153.806 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (-1+x \right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
191.611 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
224.378 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (-1+x \right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
188.330 |
|
| \begin{align*}
y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (-1+x \right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
191.743 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
258.118 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (-1+x \right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
214.412 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (-1+x \right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
223.599 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x -1\right )}{x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
157.632 |
|
| \begin{align*}
y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (-1+x \right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
158.275 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (-1+x \right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
217.194 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (x -2\right ) y}{x}&=\frac {2 a^{2} \left (-1+x \right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
210.671 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}&=-\frac {2 a^{2} \left (-1+x \right )^{2}}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
188.778 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}&=\frac {a^{2} b}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
151.261 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (-1+x \right ) \left (2+x \right )}{4 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
216.031 |
|
| \begin{align*}
y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (-1+x \right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
207.556 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (-1+x \right ) \left (3 x -4\right )}{8 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
237.404 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (-1+x \right ) \left (x -13\right )}{26 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
230.642 |
|
| \begin{align*}
y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
208.808 |
|
| \begin{align*}
y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
221.211 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
193.862 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
212.066 |
|
| \begin{align*}
y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}}&=\frac {a^{2} \left (-1+x \right ) \left (1+3 x \right )}{2 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✗ |
✗ |
235.979 |
|