# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y-a^{2} f \left (x \right )-a g \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.256 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.632 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \,x^{n} g \left (x \right ) y+a n \,x^{n -1}+a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.948 |
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+\lambda f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.315 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \] |
riccati |
[_Riccati] |
✓ |
✓ |
4.577 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.252 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.203 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-f \left (x \right ) \left ({\mathrm e}^{\lambda x} a +b \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.406 |
|
\[ {}y^{\prime } = {\mathrm e}^{\lambda x} f \left (x \right ) y^{2}+\left (a f \left (x \right )-\lambda \right ) y+b \,{\mathrm e}^{-\lambda x} f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.375 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.322 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \,{\mathrm e}^{\lambda x} g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \left (x \right )-f \left (x \right )\right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.463 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.914 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+\lambda x y+a f \left (x \right ) {\mathrm e}^{\lambda x} \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.235 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \] |
riccati |
[_Riccati] |
❇ |
N/A |
266.436 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \] |
riccati |
[_Riccati] |
❇ |
N/A |
166.462 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
49.226 |
|
\[ {}x y^{\prime } = y^{2} f \left (x \right )+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
4.026 |
|
\[ {}x y^{\prime } = f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a \] |
riccati |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.224 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.733 |
|
\[ {}y^{\prime } = -a \ln \left (x \right ) y^{2}+a f \left (x \right ) \left (x \ln \left (x \right )-x \right ) y-f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.499 |
|
\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
10.557 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
53.092 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
53.049 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \] |
riccati |
[_Riccati] |
❇ |
N/A |
176.561 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \] |
riccati |
[_Riccati] |
❇ |
N/A |
151.456 |
|
\[ {}y^{\prime } = y^{2}-f \left (x \right )^{2}+f^{\prime }\left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.621 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.8 |
|
\[ {}y^{\prime } = -f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.904 |
|
\[ {}y^{\prime } = g \left (x \right ) \left (y-f \left (x \right )\right )^{2}+f^{\prime }\left (x \right ) \] |
riccati |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
0.834 |
|
\[ {}y^{\prime } = \frac {f^{\prime }\left (x \right ) y^{2}}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.332 |
|
\[ {}f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right ) = 0 \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.255 |
|
\[ {}y^{\prime } = f^{\prime }\left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+{\mathrm e}^{\lambda x} a \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.279 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )} \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.686 |
|
\[ {}y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \] |
unknown |
[_Riccati] |
✗ |
N/A |
0.245 |
|
\[ {}y^{\prime } = y^{2}+a^{2} f \left (x a +b \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.684 |
|
\[ {}y^{\prime } = y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.774 |
|
\[ {}y^{\prime } = y^{2}+\frac {f \left (\frac {x a +b}{c x +d}\right )}{\left (c x +d \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.447 |
|
\[ {}x^{2} y^{\prime } = x^{4} f \left (x \right ) y^{2}+1 \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.27 |
|
\[ {}x^{2} y^{\prime } = x^{4} y^{2}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.606 |
|
\[ {}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+h \left (x \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.952 |
|
\[ {}y^{\prime } = y^{2}+{\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\lambda ^{2}}{4} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.012 |
|
\[ {}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{4}+\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {{\mathrm e}^{\lambda x} a +b}{c \,{\mathrm e}^{\lambda x}+d}\right )}{\left (c \,{\mathrm e}^{\lambda x}+d \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
14.124 |
|
\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
28.228 |
|
\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
10.156 |
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.028 |
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
29.443 |
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\tan \left (\lambda x \right )\right )}{\cos \left (\lambda x \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
9.927 |
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}} \] |
riccati |
[_Riccati] |
✓ |
✓ |
61.176 |
|
\[ {}y y^{\prime }-y = A \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.431 |
|
\[ {}y y^{\prime }-y = A x +B \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
19.496 |
|
\[ {}y y^{\prime }-y = -\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.157 |
|
\[ {}y y^{\prime }-y = 2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.533 |
|
\[ {}y y^{\prime }-y = A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.716 |
|
\[ {}y y^{\prime }-y = A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
0.948 |
|
\[ {}y y^{\prime }-y = \frac {A}{x}-\frac {A^{2}}{x^{3}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.587 |
|
\[ {}y y^{\prime }-y = A +B \,{\mathrm e}^{-\frac {2 x}{A}} \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.711 |
|
\[ {}y y^{\prime }-y = A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.691 |
|
\[ {}y y^{\prime }-y = -\frac {2 \left (1+m \right )}{\left (3+m \right )^{2}}+A \,x^{m} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
1.085 |
|
\[ {}y y^{\prime }-y = -\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.686 |
|
\[ {}y y^{\prime }-y = \frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (3+m \right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (3+m \right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
4.787 |
|
\[ {}y y^{\prime }-y = \frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.888 |
|
\[ {}y y^{\prime }-y = \frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.655 |
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {5 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.621 |
|
\[ {}y y^{\prime }-y = \frac {A}{x} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.483 |
|
\[ {}y y^{\prime }-y = -\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
4.425 |
|
\[ {}y y^{\prime }-y = \frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.202 |
|
\[ {}y y^{\prime }-y = 2 x +\frac {A}{x^{2}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.499 |
|
\[ {}y y^{\prime }-y = -\frac {6 X}{25}+\frac {2 A \left (2 \sqrt {x}+19 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{25} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
2.227 |
|
\[ {}y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.723 |
|
\[ {}y y^{\prime }-y = -\frac {4 x}{25}+\frac {A}{\sqrt {x}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.241 |
|
\[ {}y y^{\prime }-y = -\frac {9 x}{100}+\frac {A}{x^{\frac {5}{3}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.227 |
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.263 |
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.296 |
|
\[ {}y y^{\prime }-y = -\frac {2 x}{9}+\frac {A}{\sqrt {x}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.135 |
|
\[ {}y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{\frac {7}{5}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.399 |
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
2.559 |
|
\[ {}y y^{\prime }-y = -\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
3.225 |
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {A}{x^{\frac {5}{3}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.228 |
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
2.65 |
|
\[ {}y y^{\prime }-y = \frac {A}{\sqrt {x}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.033 |
|
\[ {}y y^{\prime }-y = \frac {A}{x^{2}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.48 |
|
\[ {}y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.729 |
|
\[ {}y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (3+2 n \right ) A^{2}}{\sqrt {x}}\right ) \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.452 |
|
\[ {}y y^{\prime }-y = A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.726 |
|
\[ {}y y^{\prime }-y = 2 A^{2}-A \sqrt {x} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.938 |
|
\[ {}y y^{\prime }-y = -\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
3.223 |
|
\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
2.659 |
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {3 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.962 |
|
\[ {}y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {b^{2}+x^{2}}}{8}+\frac {3 b^{2}}{16 \sqrt {b^{2}+x^{2}}} \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.742 |
|
\[ {}y y^{\prime }-y = \frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.853 |
|
\[ {}y y^{\prime }-y = -\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}} \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
2.006 |
|
\[ {}y y^{\prime }-y = A \,x^{2}-\frac {9}{625 A} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.58 |
|
\[ {}y y^{\prime }-y = -\frac {6}{25} x -A \,x^{2} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.482 |
|
\[ {}y y^{\prime }-y = \frac {6}{25} x -A \,x^{2} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.459 |
|
\[ {}y y^{\prime }-y = 12 x +\frac {A}{x^{\frac {5}{2}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.59 |
|
\[ {}y y^{\prime }-y = \frac {63 x}{4}+\frac {A}{x^{\frac {5}{3}}} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.24 |
|
\[ {}y y^{\prime }-y = 2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.744 |
|
\[ {}y y^{\prime }-y = 2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
2.258 |
|
\[ {}y y^{\prime }-y = -\frac {28 x}{121}+\frac {2 A \left (5 \sqrt {x}+106 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{121} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
3.323 |
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.257 |
|
|
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