Number of problems in this table is 852
|
# |
ODE |
CAS classification |
Solved? |
Verified? |
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x +1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \left (-2+x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{x^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{\sqrt {2+x}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \sqrt {x^{2}+9} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {10}{x^{2}+1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \cos \left (2 x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{\sqrt {-x^{2}+1}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \,{\mathrm e}^{-x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x^{2} y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{\frac {1}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = -1+x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \ln \left (1+y \left (x \right )^{2}\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{x} y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x^{2} \left (1+y \left (x \right )^{2}\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \frac {x}{\sqrt {x^{2}-16}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -y \left (x \right )+4 x^{3} y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}1+\frac {d}{d x}y \left (x \right ) = 2 y \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}-y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x^{2} y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x y \left (x \right )^{2}+3 x^{2} y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 6 \,{\mathrm e}^{2 x -y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 \sqrt {x}\, \left (\frac {d}{d x}y \left (x \right )\right ) = \cos \left (y \left (x \right )\right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = 2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = 3 \,{\mathrm e}^{2 x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 3 x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )+2 x \left (\frac {d}{d x}y \left (x \right )\right ) = 10 \sqrt {x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}-y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = 3 x y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}3 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x^{5} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = {\mathrm e}^{x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-3 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = x^{3} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 x y \left (x \right ) = x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \cos \left (x \right ) \left (1-y \left (x \right )\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )+\left (1+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \cos \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+x +y \left (x \right )+x y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = x^{4} \cos \left (x \right )+3 y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x^{2} {\mathrm e}^{x^{2}}+2 x y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}3 x y \left (x \right )+\left (x^{2}+4\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}3 x^{3} y \left (x \right )+\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}-y \left (t \right )+y^{\prime }\left (t \right ) = 2 t \,{\mathrm e}^{2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = t \,{\mathrm e}^{-2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+t y^{\prime }\left (t \right ) = t^{2}-t +1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {2 y \left (t \right )}{t}+y^{\prime }\left (t \right ) = \frac {\cos \left (t \right )}{t^{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}-2 y \left (t \right )+y^{\prime }\left (t \right ) = {\mathrm e}^{2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+t y^{\prime }\left (t \right ) = \sin \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}4 t^{2} y \left (t \right )+t^{3} y^{\prime }\left (t \right ) = {\mathrm e}^{-t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (t +1\right ) y \left (t \right )+t y^{\prime }\left (t \right ) = t \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}-\frac {y \left (t \right )}{2}+y^{\prime }\left (t \right ) = 2 \cos \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-y \left (t \right )+2 y^{\prime }\left (t \right ) = {\mathrm e}^{\frac {t}{3}} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (t \right )+3 y^{\prime }\left (t \right ) = {\mathrm e}^{-\frac {\pi t}{2}} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\left (t +1\right ) y \left (t \right )+t y^{\prime }\left (t \right ) = 2 t \,{\mathrm e}^{-t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+t y^{\prime }\left (t \right ) = \frac {\sin \left (t \right )}{t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\cos \left (t \right ) y \left (t \right )+\sin \left (t \right ) y^{\prime }\left (t \right ) = {\mathrm e}^{t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {y \left (t \right )}{2}+y^{\prime }\left (t \right ) = 2 \cos \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {y \left (t \right )}{4}+y^{\prime }\left (t \right ) = 3+2 \cos \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \left (1-2 x \right ) y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1-2 x}{y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x +y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) {\mathrm e}^{-x} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}r \left (x \right ) = \frac {r \left (x \right )^{2}}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x}{y \left (x \right )+x^{2} y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x y \left (x \right )^{2}}{\sqrt {x^{2}+1}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x}{1+2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x \left (x^{2}+1\right )}{4 y \left (x \right )^{3}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\sin \left (2 x \right )+\cos \left (3 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\sqrt {-x^{2}+1}\, y \left (x \right )^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = \arcsin \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {3 x^{2}+1}{-6 y \left (x \right )+3 y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 y \left (x \right )^{2}+x y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2-{\mathrm e}^{x}}{3+2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 \cos \left (2 x \right )}{3+2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 \left (1+x \right ) \left (1+y \left (x \right )^{2}\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y \left (t \right )+\left (t -4\right ) t y^{\prime }\left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\tan \left (t \right ) y \left (t \right )+y^{\prime }\left (t \right ) = \sin \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 t y \left (t \right )+\left (-t^{2}+4\right ) y^{\prime }\left (t \right ) = 3 t^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 t y \left (t \right )+\left (-t^{2}+4\right ) y^{\prime }\left (t \right ) = 3 t^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 x -y \left (x \right )+\left (-x +2 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-1+9 x^{2}+y \left (x \right )+\left (x -4 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )+2 x}{3-x +3 y \left (x \right )^{2}} \] |
[_rational] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 1-y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = \frac {\sin \left (x \right )}{x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x +y \left (x \right )+\left (2 y \left (x \right )+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x^{2}-1}{1+y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -x \,{\mathrm e}^{x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \sin \left (x^{2}\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x^{2}-2 x^{2} y \left (x \right )+2}{x^{3}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \left (1+y \left (x \right )^{2}\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {y \left (x \right ) \left (y \left (x \right )+1\right )}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {\left (1+x \right ) y \left (x \right )}{x} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+\left (1+\frac {1}{\ln \left (x \right )}\right ) y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-\frac {2 x y \left (x \right )}{x^{2}+1} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {k y \left (x \right )}{x} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+7 y \left (x \right ) = {\mathrm e}^{3 x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+4 x y \left (x \right ) = \frac {2}{x^{2}+1} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}3 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = \frac {2}{x \left (x^{2}+1\right )} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) \cot \left (x \right ) = \cos \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {y \left (x \right )}{x} = \frac {2}{x^{2}}+1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+3 y \left (x \right ) = \frac {1}{\left (-1+x \right )^{3}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 8 x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )-2 y \left (x \right ) = -x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 x y \left (x \right ) = x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+4 y \left (x \right ) = \frac {2 x^{2}+1}{x \left (2+x \right )^{3}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) \left (\frac {d}{d x}y \left (x \right )\right )-2 x y \left (x \right ) = x \left (x^{2}-1\right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x^{2}+3 x +2}{y \left (x \right )-2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+x \left (y \left (x \right )^{2}+y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (3 y \left (x \right )^{2}+4 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right )+2 x +\cos \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {\left (y \left (x \right )+1\right ) \left (y \left (x \right )-1\right ) \left (y \left (x \right )-2\right )}{1+x} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 x \left (y \left (x \right )+1\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x y \left (x \right ) \left (1+y \left (x \right )^{2}\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -2 x \left (y \left (x \right )^{3}-3 y \left (x \right )+2\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x}{1+2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 y \left (x \right )-y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x +y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) \left (-2+x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\cos \left (x \right )}{\sin \left (y \left (x \right )\right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{\frac {2}{5}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x \left (y \left (x \right )-1\right )^{\frac {1}{3}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}+x y \left (x \right )-x^{2} \] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = x y \left (x \right )^{3} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-x y \left (x \right ) = x y \left (x \right )^{\frac {3}{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = x^{4} y \left (x \right )^{4} \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = 2 \sqrt {y \left (x \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-4 y \left (x \right ) = \frac {48 x}{y \left (x \right )^{2}} \] |
[_rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+2 x y \left (x \right ) = y \left (x \right )^{3} \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-y \left (x \right ) = x \sqrt {y \left (x \right )} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x y \left (x \right )+y \left (x \right )^{2}}{x^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x^{3}+y \left (x \right )^{3}}{x y \left (x \right )^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+x^{2}+y \left (x \right )^{2} = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )^{2}-3 x y \left (x \right )-5 x^{2}}{x^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x^{2}+y \left (x \right )^{2}+4 x y \left (x \right ) \] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 3 x^{2}+4 y \left (x \right )^{2} \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}+x y \left (x \right )-4 x^{2} \] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {2 y \left (x \right )}{x} = \frac {3 x^{2} y \left (x \right )^{2}+6 x y \left (x \right )+2}{x^{2} \left (2 x y \left (x \right )+3\right )} \] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {3 y \left (x \right )}{x} = \frac {3 x^{4} y \left (x \right )^{2}+10 x^{2} y \left (x \right )+6}{x^{3} \left (2 x^{2} y \left (x \right )+5\right )} \] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}4 x^{3} y \left (x \right )^{2}-6 x^{2} y \left (x \right )-2 x -3+\left (2 x^{4} y \left (x \right )-2 x^{3}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}\left (2 x -1\right ) \left (y \left (x \right )-1\right )+\left (2+x \right ) \left (x -3\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+\sin \left (t \right ) y \left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+{\mathrm e}^{t^{2}} y \left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+2 t y \left (t \right ) = t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \frac {1}{t^{2}+1} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\sqrt {t^{2}+1}\, y \left (t \right )+y^{\prime }\left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}-2 t y \left (t \right )+y^{\prime }\left (t \right ) = t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}t y \left (t \right )+y^{\prime }\left (t \right ) = t +1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \frac {1}{t^{2}+1} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}-2 t y \left (t \right )+y^{\prime }\left (t \right ) = 1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}4 t y \left (t \right )+\left (t^{2}+1\right ) y^{\prime }\left (t \right ) = t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}t^{2} \left (1+y \left (t \right )^{2}\right )+2 y \left (t \right ) y^{\prime }\left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {2 t}{t^{2} y \left (t \right )+y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\sqrt {t^{2}+1}\, y^{\prime }\left (t \right ) = \frac {t y \left (t \right )^{3}}{\sqrt {t^{2}+1}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {3 t^{2}+4 t +2}{-2+2 y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = k \left (a -y \left (t \right )\right ) \left (b -y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}3 t y^{\prime }\left (t \right ) = \cos \left (t \right ) y \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right ) = y \left (t \right )+\sqrt {t^{2}+y \left (t \right )^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}2 t y \left (t \right )^{3}+3 t^{2} y \left (t \right )^{2} y^{\prime }\left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}3 t^{2}+4 t y \left (t \right )+\left (2 t^{2}+2 y \left (t \right )\right ) y^{\prime }\left (t \right ) = 0 \] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}3 t y \left (t \right )+y \left (t \right )^{2}+\left (t y \left (t \right )+t^{2}\right ) y^{\prime }\left (t \right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )^{2} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{y \left (x \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}{\mathrm e}^{y \left (x \right )} \left (1+\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}1+y \left (x \right )^{2} = \frac {\frac {d}{d x}y \left (x \right )}{x^{3} \left (-1+x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2}+3 x \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{3}+2 y \left (x \right ) \] |
[_rational, _Abel] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}+x +1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}+2 y \left (x \right )+5 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x -8\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}+y \left (x \right )-2 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \,{\mathrm e}^{\frac {y \left (x \right )}{x}}+y \left (x \right ) = x \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x +y \left (x \right )}{x -y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\left (3 x y \left (x \right )-2 x^{2}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 2 y \left (x \right )^{2}-x y \left (x \right ) \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}3 x -y \left (x \right )+1+\left (x -3 y \left (x \right )-5\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}6 x -3 y \left (x \right )+6+\left (2 x -y \left (x \right )+5\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x +3 y \left (x \right )+2+\left (y \left (x \right )-x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x +y \left (x \right )+4 = \left (2 x +2 y \left (x \right )-1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x +3 y \left (x \right )-1+\left (2 x +3 y \left (x \right )+2\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}3 x -y \left (x \right )+2+\left (x +2 y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}3 x +2 y \left (x \right )+3-\left (x +2 y \left (x \right )-1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x -2 y \left (x \right )+3+\left (1-x +2 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x +y \left (x \right )+\left (4 x +2 y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x +y \left (x \right )+\left (4 x -2 y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (1-x^{4} y \left (x \right )^{2}\right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y \left (x \right )+x \left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} y \left (x \right )^{2}-y \left (x \right )+\left (2 x^{3} y \left (x \right )+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+y \left (x \right )^{2}-2 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x \] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )^{2}+1+\left (2 x y \left (x \right )-y \left (x \right )^{2}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )+y \left (x \right )^{3}+4 \left (x y \left (x \right )^{2}-1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )-x y \left (x \right )-3+x \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+\left (x^{2}-1\right )^{2}+4 y \left (x \right ) = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = y \left (t \right )^{2} {\mathrm e}^{-t} \] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \left (1-{\mathrm e}^{2 y \left (x \right )-x^{2}}\right ) \] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right ) = \left (y \left (x \right )^{4} x^{2}+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right ) = x \left (-x^{2}+1\right ) \sqrt {y \left (x \right )} \] |
[_rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x \sqrt {1-y \left (x \right )}-\sqrt {-x^{2}+1}\, \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right )-y \left (x \right )^{2}-x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )-2 y \left (x \right )-2 x^{4} y \left (x \right )^{3} = 0 \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\left (-2 x^{2}-3 x y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )^{2} = 0 \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = x^{4}+4 y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = x^{3} y \left (x \right )^{6} \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d \theta }x \left (\theta \right ) = x \left (\theta \right )+x \left (\theta \right )^{2} {\mathrm e}^{\theta } \] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
|
|
\[ {}3 x y \left (x \right )+\left (3 x^{2}+y \left (x \right )^{2}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = 3 \,{\mathrm e}^{2 x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}4 x y \left (x \right )^{2}+\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x -2 y \left (x \right )+3 = \left (x -2 y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x y \left (x \right )-2 y \left (x \right )+1+x \left (-1+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )^{3}+2 x^{2} y \left (x \right )+\left (-3 x^{3}-2 x y \left (x \right )^{2}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}2 \left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \left (2 y \left (x \right )^{2}-1\right ) x y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {1-y \left (x \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )-x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2} y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x +\frac {y \left (x \right )}{x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2}+y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )-4 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -y \left (t \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {{\mathrm e}^{t}}{y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t \,{\mathrm e}^{2 t} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sin \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 8 \,{\mathrm e}^{4 t}+t \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right ) = y \left (t \right )+t^{3} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {2 y \left (t \right )}{t +1} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right ) = -y \left (t \right )+t^{3} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+4 \tan \left (2 t \right ) y \left (t \right ) = \tan \left (2 t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}t \ln \left (t \right ) y^{\prime }\left (t \right ) = \ln \left (t \right ) t -y \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {2 y \left (t \right )}{-t^{2}+1}+3 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -\cot \left (t \right ) y \left (t \right )+6 \cos \left (t \right )^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-\frac {y \left (x \right )}{x} = 1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-y \left (x \right ) \tan \left (x \right ) = 1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-\frac {y \left (x \right )^{2}}{x^{2}} = {\frac {1}{4}} \] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
|
|
\[ {}\left (\frac {d}{d x}y \left (x \right )\right ) \sin \left (x \right )+2 y \left (x \right ) \cos \left (x \right ) = 1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )-\frac {y \left (x \right )^{2}}{x^{\frac {3}{2}}} = 0 \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )^{2} = -1 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right ) = x a \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1-\frac {\sin \left (x +y \left (x \right )\right )}{\sin \left (y \left (x \right )\right ) \cos \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\left (1-y \left (x \right ) {\mathrm e}^{x y \left (x \right )}\right ) {\mathrm e}^{-x y \left (x \right )}}{x} \] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\cos \left (x \right )-2 x y \left (x \right )^{2}}{2 x^{2} y \left (x \right )} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \ln \left (x \right ) x^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )^{2} = -1 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right ) = x a \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1-\frac {\sin \left (x +y \left (x \right )\right )}{\sin \left (y \left (x \right )\right ) \cos \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{3} \sin \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}m v^{\prime }\left (t \right ) = m g -k v \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {2 y \left (x \right )}{x} = 4 x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (\frac {d}{d x}y \left (x \right )\right ) \sin \left (x \right )-y \left (x \right ) \cos \left (x \right ) = \sin \left (2 x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+\frac {2 x \left (t \right )}{4-t} = 5 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )-{\mathrm e}^{x}+\frac {d}{d x}y \left (x \right ) = 0 \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[
{}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {-2 x +4 y \left (x \right )}{x +y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x -y \left (x \right )}{x +4 y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )-\sqrt {x^{2}+y \left (x \right )^{2}}}{x} \] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x +\frac {y \left (x \right )}{2}}{\frac {x}{2}-y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {2 x y \left (x \right )}{x^{2}+1} = x y \left (x \right )^{2} \] |
[_rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) \cot \left (x \right ) = y \left (x \right )^{3} \sin \left (x \right )^{3} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \left (9 x -y \left (x \right )\right )^{2} \] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x \left (x +y \left (x \right )\right )^{2}-1 \] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
|
|
\[ {}\frac {\frac {d}{d x}y \left (x \right )}{y \left (x \right )}-\frac {2 \ln \left (y \left (x \right )\right )}{x} = \frac {1-2 \ln \left (x \right )}{x} \] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}-2 y \left (t \right )+y^{\prime }\left (t \right ) = 6 \,{\mathrm e}^{5 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = 8 \,{\mathrm e}^{3 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+3 y \left (t \right ) = 2 \,{\mathrm e}^{-t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = 4 t \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 6 \cos \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 5 \sin \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = 5 \,{\mathrm e}^{t} \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = 2 \operatorname {Heaviside}\left (-1+t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (t \right )+y^{\prime }\left (t \right ) = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+3 y \left (t \right ) = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-3 y \left (t \right ) = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \delta \left (t -5\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (t \right )+y^{\prime }\left (t \right ) = \delta \left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+4 y \left (t \right ) = 3 \delta \left (-1+t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-5 y \left (t \right ) = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}6 x +4 y \left (x \right )+1+\left (4 x +2 y \left (x \right )+2\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}3 x -y \left (x \right )-6+\left (x +y \left (x \right )+2\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x +3 y \left (x \right )+1+\left (4 x +6 y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-y \left (x \right ) \tan \left (x \right ) = x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{x -2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = x +y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}{\mathrm e}^{-y \left (x \right )}+\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{x} \sin \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-3 y \left (x \right ) = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +\frac {1}{x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = \left (3 x +2\right ) {\mathrm e}^{3 x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 \sin \left (3 x \right ) \sin \left (2 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right )-3 \cos \left (3 x \right ) \cos \left (2 y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \left (1+x \right ) \left (y \left (x \right )+1\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x -y \left (x \right )}{y \left (x \right )+2 x} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {3 x -y \left (x \right )+1}{3 y \left (x \right )-x +5} \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}3 y \left (x \right )-7 x +7+\left (7 y \left (x \right )-3 x +3\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\cos \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) \sin \left (x \right ) = 1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (x +y \left (x \right )^{2}\right ) \left (\frac {d}{d x}y \left (x \right )\right )-x^{2}+y \left (x \right ) = 0 \] |
[_exact, _rational] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )-y \left (x \right )^{2} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 x y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \,{\mathrm e}^{-2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-2 x y \left (x \right ) = 2 x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = x y \left (x \right )+y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \cos \left (y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1+\sin \left (y \left (x \right )\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = 2 y \left (x \right ) \left (y \left (x \right )-1\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 x \left (\frac {d}{d x}y \left (x \right )\right ) = 1-y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}{\mathrm e}^{2 x} y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+2 x = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \sqrt {y \left (x \right )^{2}-9} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {x}{x^{2}+y \left (x \right )^{2}}+\frac {y \left (x \right )}{x^{2}}+\left (\frac {y \left (x \right )}{x^{2}+y \left (x \right )^{2}}-\frac {1}{x}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x \left (1+y \left (x \right )^{2}\right )}{y \left (x \right ) \left (x^{2}+1\right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \,{\mathrm e}^{\frac {y \left (x \right )}{x}}+y \left (x \right ) = x \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right )-y \left (x \right )^{2}-x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x +y \left (x \right )+\left (3 x +3 y \left (x \right )-4\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )+7+\left (2 x +y \left (x \right )+3\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\sin \left (x \right ) \cos \left (y \left (x \right )\right )+\cos \left (x \right ) \sin \left (y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-y \left (x \right ) = {\mathrm e}^{x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {y \left (x \right )}{x} = \frac {y \left (x \right )^{2}}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 \cos \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right ) \sin \left (x \right )-y \left (x \right )^{3} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \sqrt {1-y \left (x \right )^{2}}+y \left (x \right ) \sqrt {-x^{2}+1}\, \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )-x y \left (x \right ) = y \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right )^{2}-8 x = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 x y \left (x \right )^{2} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-x y \left (x \right ) = x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 \frac {d}{d x}y \left (x \right ) = 3 \left (y \left (x \right )-2\right )^{\frac {1}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (x +x y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y \left (x \right )+x^{3} \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}-y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{3} \left (1-y \left (x \right )\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {\frac {d}{d x}y \left (x \right )}{2} = \sqrt {y \left (x \right )+1}\, \cos \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = \frac {4 x^{2}-x -2}{\left (1+x \right ) \left (y \left (x \right )+1\right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {\frac {d}{d \theta }y \left (\theta \right )}{\theta } = \frac {y \left (\theta \right ) \sin \left (\theta \right )}{y \left (\theta \right )^{2}+1} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2}+2 y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 t \cos \left (y \left (t \right )\right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 8 x^{3} {\mathrm e}^{-2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2} \left (y \left (x \right )+1\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\sqrt {y \left (x \right )}+\left (1+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{x^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {{\mathrm e}^{x^{2}}}{y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {\sin \left (x \right )+1}\, \left (1+y \left (x \right )^{2}\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 t y \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )^{3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )^{3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )^{3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{2}-3 y \left (x \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-\frac {y \left (x \right )}{x} = x \,{\mathrm e}^{x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+4 y \left (x \right )-{\mathrm e}^{-x} = 0 \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime }\left (t \right )+3 x \left (t \right ) t = t^{4} \ln \left (t \right )+1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {3 y \left (x \right )}{x}+2 = 3 x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (\frac {d}{d x}y \left (x \right )\right ) \sin \left (x \right )+y \left (x \right ) \cos \left (x \right ) = x \sin \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) \sqrt {1+\sin \left (x \right )^{2}} = x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+\sin \left (t \right ) x \left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-{\mathrm e}^{x} y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+2 x y \left (x \right )-x +1 = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = \left (1+x \right )^{2} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+2 x y \left (x \right ) = \sinh \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = x^{2} y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}-y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = x^{3} \cos \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+3 x y \left (x \right ) = 5 x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 3 x -1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}-x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{3 x -2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {y \left (x \right )}{x} = \sin \left (2 x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x -2 y \left (x \right )+1}{2 x -4 y \left (x \right )} \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {y \left (x \right )}{x} = \sin \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+x +x y \left (x \right )^{2} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = 2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = {\mathrm e}^{x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+x^{2}+y \left (x \right )^{2} = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )^{2}+x y \left (x \right )-x \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = 2 y \left (x \right )+x^{3} {\mathrm e}^{x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}L i^{\prime }\left (t \right )+R i \left (t \right ) = E \sin \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+4 y \left (x \right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = x y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+\frac {26 y \left (t \right )}{5} = \frac {97 \sin \left (2 t \right )}{5} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-6 y \left (t \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+2 x y \left (x \right )^{2} = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {3 x^{2}+4 x +2}{2 y \left (x \right )-2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (2 y \left (x \right )+x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {3 x^{2}+4 x +2}{2 y \left (x \right )-2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}L \left (\frac {d}{d x}y \left (x \right )\right )+R y \left (x \right ) = E \sin \left (\omega x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}L \left (\frac {d}{d x}y \left (x \right )\right )+R y \left (x \right ) = E \,{\mathrm e}^{i \omega x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )+1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \,{\mathrm e}^{x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 \sin \left (x \right ) \cos \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \ln \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}-4\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) \left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x^{2}+x \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1+x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {\frac {d}{d x}y \left (x \right )}{x^{2}+1} = \frac {x}{y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
|
||||
|
\[ {}y \left (x \right )^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = 2+x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2} y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = -x^{2}+1 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-x y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-2 x y \left (x \right ) = 6 x \,{\mathrm e}^{x^{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-\frac {y \left (x \right )}{x} = x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+4 y \left (x \right ) = {\mathrm e}^{-x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right ) = 2 x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}-y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )-2 y \left (x \right ) = 3 x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\csc \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \csc \left (y \left (x \right )\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 x \cos \left (y \left (x \right )\right )-x^{2} \sin \left (y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x -y \left (x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x -y \left (x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}L i^{\prime }\left (t \right )+R i \left (t \right ) = E_{0} \sin \left (\omega t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -x +y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -x +y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = x^{2} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = x^{2} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime }\left (t \right )+y \left (t \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+6 y \left (t \right ) = {\mathrm e}^{4 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 2 \cos \left (5 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+4 y \left (t \right ) = {\mathrm e}^{-4 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 1+t \,{\mathrm e}^{t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = t \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = t \,{\mathrm e}^{t} \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-3 y \left (t \right ) = \delta \left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \delta \left (-1+t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )^{2} = -1 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x -y \left (x \right )}{x +4 y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {\frac {y \left (x \right )+1}{y \left (x \right )^{2}}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1}{1-y \left (t \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 y \left (x \right ) \left (x \sqrt {y \left (x \right )}-1\right ) \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d z}w \left (z \right ) = -\frac {1}{2}-\frac {\sqrt {1-12 w \left (z \right )}}{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = t \cos \left (t^{2}\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \frac {t +1}{\sqrt {t}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \sqrt {x \left (t \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = {\mathrm e}^{-2 x \left (t \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1}{2 y \left (t \right )+1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \left (4 t -x \left (t \right )\right )^{2} \] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = 2 t x \left (t \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = t^{2} {\mathrm e}^{-x \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = x \left (t \right ) \left (4+x \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = {\mathrm e}^{t +x \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}T^{\prime }\left (t \right ) = 2 a t \left (T \left (t \right )^{2}-a^{2}\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t^{2} \tan \left (y \left (t \right )\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \frac {\left (4+2 t \right ) x \left (t \right )}{\ln \left (x \left (t \right )\right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {2 t y \left (t \right )^{2}}{t^{2}+1} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) {\mathrm e}^{2 t}+2 x \left (t \right ) {\mathrm e}^{2 t} = {\mathrm e}^{-t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -y \left (t \right )^{2} {\mathrm e}^{-t^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+\frac {5 x \left (t \right )}{t} = t +1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \left (a +\frac {b}{t}\right ) x \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}R^{\prime }\left (t \right )+\frac {R \left (t \right )}{t} = \frac {2}{t^{2}+1} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}R^{\prime }\left (t \right ) = \frac {R \left (t \right )}{t}+t \,{\mathrm e}^{-t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+\frac {{\mathrm e}^{-t} x \left (t \right )}{t} = t \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+5 x \left (t \right ) = \operatorname {Heaviside}\left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+x \left (t \right ) = \sin \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = 2 x \left (t \right )+\operatorname {Heaviside}\left (-1+t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = x \left (t \right )-2 \operatorname {Heaviside}\left (-1+t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = -x \left (t \right )+\operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+3 x \left (t \right ) = \delta \left (-1+t \right )+\operatorname {Heaviside}\left (t -4\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = 2 x \,{\mathrm e}^{-x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = 2 x \,{\mathrm e}^{-x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2} \sin \left (y \left (x \right )\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )^{2}}{-2+x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 x y \left (x \right )-3+\left (x^{2}+4 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {3-y \left (x \right )}{x^{2}}+\frac {\left (y \left (x \right )^{2}-2 x \right ) \left (\frac {d}{d x}y \left (x \right )\right )}{x y \left (x \right )^{2}} = 0 \] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
|
|
\[ {}\frac {1+8 x y \left (x \right )^{\frac {2}{3}}}{x^{\frac {2}{3}} y \left (x \right )^{\frac {1}{3}}}+\frac {\left (2 x^{\frac {4}{3}} y \left (x \right )^{\frac {2}{3}}-x^{\frac {1}{3}}\right ) \left (\frac {d}{d x}y \left (x \right )\right )}{y \left (x \right )^{\frac {4}{3}}} = 0 \] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )+2+y \left (x \right ) \left (x +4\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}8 \cos \left (y \left (x \right )\right )^{2}+\csc \left (x \right )^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (3 x +8\right ) \left (y \left (x \right )^{2}+4\right )-4 y \left (x \right ) \left (x^{2}+5 x +6\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2}+3 y \left (x \right )^{2}-2 x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}3 x^{2}+9 x y \left (x \right )+5 y \left (x \right )^{2}-\left (6 x^{2}+4 x y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )-2 y \left (x \right ) = 2 x^{4} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+3 x^{2} y \left (x \right ) = x^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}2 x \left (y \left (x \right )+1\right )-\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}r^{\prime }\left (t \right )+r \left (t \right ) \tan \left (t \right ) = \cos \left (t \right )^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )-x \left (t \right ) = \sin \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {y \left (x \right )}{2 x} = \frac {x}{y \left (x \right )^{3}} \] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = \left (x y \left (x \right )\right )^{\frac {3}{2}} \] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{2}+y \left (x \right )^{2}-2 x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}{\mathrm e}^{2 x} y \left (x \right )^{2}-2 x +{\mathrm e}^{2 x} y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}3 x^{2}+2 x y \left (x \right )^{2}+\left (2 x^{2} y \left (x \right )+6 y \left (x \right )^{2}\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact, _rational] |
✓ |
✓ |
|
|
\[ {}4 x y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1+y \left (x \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x +7 y \left (x \right )}{2 x -2 y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x y \left (x \right )}{x^{2}+1} \] |
[_separable] |
✓ |
✓ |
|
|
\[
{}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[
{}\left (2+x \right ) \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2 |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right ) = \frac {y \left (x \right )^{3}}{x} \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}6 x +4 y \left (x \right )+1+\left (4 x +2 y \left (x \right )+2\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}3 x -y \left (x \right )-6+\left (x +y \left (x \right )+2\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x +3 y \left (x \right )+1+\left (4 x +6 y \left (x \right )+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \sec \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x -\frac {1}{3} x^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = 2 \sin \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}V \left (x \right )\right ) = x^{2}+1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) {\mathrm e}^{3 t}+3 x \left (t \right ) {\mathrm e}^{3 t} = {\mathrm e}^{-t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = t^{3} \left (-x \left (t \right )+1\right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \left (1+y \left (x \right )^{2}\right ) \tan \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+x \left (t \right ) t = 4 t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) {\mathrm e}^{-x} = 1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) \cot \left (x \right ) = 5 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+\left (a +\frac {1}{t}\right ) x \left (t \right ) = b \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )^{3}+x^{2} \] |
[_Abel] |
✗ |
N/A |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x -y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+5 x \left (t \right ) = 10 t +2 \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \frac {x \left (t \right )}{t}+\frac {x \left (t \right )^{2}}{t^{3}} \] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-2 y \left (t \right ) = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}10 Q^{\prime }\left (t \right )+100 Q \left (t \right ) = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+\frac {y \left (x \right )}{x} = {\mathrm e}^{x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 4 y \left (x \right )-5 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+3 y \left (x \right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2}+{\mathrm e}^{x}-\sin \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )+\frac {1}{x^{2}+1} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x}+\cos \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x}+\tan \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{-x^{2}+4}+\sqrt {x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{-x^{2}+4}+\sqrt {x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right ) \cot \left (x \right )+\csc \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+3 x \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +\frac {1}{x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 \sin \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \sin \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{-1+x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{-1+x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{x^{2}-1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{x^{2}-1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \tan \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \tan \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 y \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1-y \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1-y \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \,{\mathrm e}^{-x^{2}+y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 x}{y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -2 y \left (x \right )+y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +x y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \,{\mathrm e}^{y \left (x \right )}+\frac {d}{d x}y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y \left (x \right )-x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 4 y \left (x \right )+1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x y \left (x \right )+2 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{-1+x}+x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x}+\sin \left (x^{2}\right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 y \left (x \right )}{x}+{\mathrm e}^{x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right ) \cot \left (x \right )+\sin \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{-1+x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +y \left (x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{-x^{2}+1}+\sqrt {x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{-x^{2}+1}+\sqrt {x} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {3 x^{2}}{2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {3 x^{2}}{2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {3 x^{2}}{2 y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\sqrt {y \left (x \right )}}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\sqrt {y \left (x \right )}}{x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x y \left (x \right )^{\frac {1}{3}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x y \left (x \right )^{\frac {1}{3}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 x y \left (x \right )^{\frac {1}{3}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {\left (y \left (x \right )+2\right ) \left (y \left (x \right )-1\right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{y \left (x \right )-x} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{y \left (x \right )-x} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{y \left (x \right )-x} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x y \left (x \right )}{x^{2}+y \left (x \right )^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x y \left (x \right )}{x^{2}+y \left (x \right )^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \sqrt {1-y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \sqrt {1-y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \sqrt {1-y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y \left (x \right )}}{2} \] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-i y \left (x \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-y \left (x \right ) = 2 \,{\mathrm e}^{x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = 6 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) = {\mathrm e}^{x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+3 y \left (x \right ) = \delta \left (-2+x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-3 y \left (x \right ) = \delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (-2+x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = -x \left (t \right ) t \] |
[_separable] |
✓ |
✓ |
|
|
|
||||
|
\[ {}y^{\prime }\left (t \right ) = t y \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -y \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t^{2} y \left (t \right )^{3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -y \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {t}{y \left (t \right )-t^{2} y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )+1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t y \left (t \right )^{2}+2 y \left (t \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = \frac {t^{2}}{x \left (t \right )+t^{3} x \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1-y \left (t \right )^{2}}{y \left (t \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \left (1+y \left (t \right )^{2}\right ) t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1}{2 y \left (t \right )+3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 t y \left (t \right )^{2}+3 t^{2} y \left (t \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {y \left (t \right )^{2}+5}{y \left (t \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 y \left (t \right ) \left (1-y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )-t \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \left (y \left (t \right )+\frac {1}{2}\right ) \left (t +y \left (t \right )\right ) \] |
[_Riccati] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \left (t +1\right ) y \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}S^{\prime }\left (t \right ) = S \left (t \right )^{3}-2 S \left (t \right )^{2}+S \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}S^{\prime }\left (t \right ) = S \left (t \right )^{3}-2 S \left (t \right )^{2}+S \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}S^{\prime }\left (t \right ) = S \left (t \right )^{3}-2 S \left (t \right )^{2}+S \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}S^{\prime }\left (t \right ) = S \left (t \right )^{3}-2 S \left (t \right )^{2}+S \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}S^{\prime }\left (t \right ) = S \left (t \right )^{3}-2 S \left (t \right )^{2}+S \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )+1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t -y \left (t \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 t \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sin \left (y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}w^{\prime }\left (t \right ) = \left (3-w \left (t \right )\right ) \left (w \left (t \right )+1\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}w^{\prime }\left (t \right ) = \left (3-w \left (t \right )\right ) \left (w \left (t \right )+1\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = {\mathrm e}^{\frac {2}{y \left (t \right )}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = {\mathrm e}^{\frac {2}{y \left (t \right )}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-y \left (t \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )^{3}+t^{2} \] |
[_Abel] |
✗ |
N/A |
|
|
\[ {}y^{\prime }\left (t \right ) = \sqrt {y \left (t \right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2-y \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\theta ^{\prime }\left (t \right ) = \frac {9}{10}-\frac {11 \cos \left (\theta \left (t \right )\right )}{10} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right ) \left (y \left (t \right )-1\right ) \left (y \left (t \right )-3\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right ) \left (y \left (t \right )-1\right ) \left (y \left (t \right )-3\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right ) \left (y \left (t \right )-1\right ) \left (y \left (t \right )-3\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right ) \left (y \left (t \right )-1\right ) \left (y \left (t \right )-3\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1}{\left (y \left (t \right )+1\right ) \left (t -2\right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1}{\left (y \left (t \right )+2\right )^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {t}{y \left (t \right )-2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 y \left (t \right ) \left (y \left (t \right )-2\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 y \left (t \right ) \left (y \left (t \right )-2\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 y \left (t \right ) \left (y \left (t \right )-2\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 y \left (t \right ) \left (y \left (t \right )-2\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )-12 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )-12 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )-12 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )-12 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}w^{\prime }\left (t \right ) = w \left (t \right ) \cos \left (w \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}w^{\prime }\left (t \right ) = w \left (t \right ) \cos \left (w \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}w^{\prime }\left (t \right ) = w \left (t \right ) \cos \left (w \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}w^{\prime }\left (t \right ) = w \left (t \right ) \cos \left (w \left (t \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-4 y \left (t \right )+2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = {\mathrm e}^{\frac {t}{3}} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-2 y \left (t \right ) = 3 \,{\mathrm e}^{-2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+3 y \left (t \right ) = \cos \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-2 y \left (t \right ) = 7 \,{\mathrm e}^{2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -\frac {y \left (t \right )}{t +1}+2 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{t +1}+4 t^{2}+4 t \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -\frac {y \left (t \right )}{t}+2 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -2 t y \left (t \right )+4 \,{\mathrm e}^{-t^{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-\frac {2 y \left (t \right )}{t} = 2 t^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-\frac {3 y \left (t \right )}{t} = 2 t^{3} {\mathrm e}^{2 t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = -x \left (t \right ) t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 y \left (t \right )+\cos \left (4 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 y \left (t \right )+2 \,{\mathrm e}^{3 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t^{2} y \left (t \right )^{3}+y \left (t \right )^{3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+5 y \left (t \right ) = 3 \,{\mathrm e}^{-5 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 t y \left (t \right )+3 t \,{\mathrm e}^{t^{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {\left (t +1\right )^{2}}{\left (y \left (t \right )+1\right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 2 t y \left (t \right )^{2}+3 t^{2} y \left (t \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 1-y \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {t^{2}}{y \left (t \right )+t^{3} y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2}-2 y \left (t \right )+1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3-y \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 40 \,{\mathrm e}^{2 x} x \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (6+x \right )^{\frac {1}{3}} \left (\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {-1+x}{1+x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+2 = \sqrt {x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\cos \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )-\sin \left (x \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sin \left (\frac {x}{2}\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sin \left (\frac {x}{2}\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 \sqrt {x +3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 \sqrt {x +3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 3 \sqrt {x +3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x \,{\mathrm e}^{-x^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x}{\sqrt {x^{2}+5}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{x^{2}+1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{-9 x^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x}{y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x -1+2 x y \left (x \right )-y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = x y \left (x \right )^{2}+x \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 3 \sqrt {x y \left (x \right )^{2}+9 x} \] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
|
|
\[ {}-2 y \left (x \right )+\frac {d}{d x}y \left (x \right ) = -10 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right ) = \sin \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 x -1+2 x y \left (x \right )-y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}-y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )^{2}-y \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )^{2}-1}{x y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-3 y \left (x \right ) = 6 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-3 y \left (x \right ) = 6 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+5 y \left (x \right ) = {\mathrm e}^{-3 x} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+3 y \left (x \right ) = 20 x^{2} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right )+x^{2} \cos \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = x \left (3+3 x^{2}-y \left (x \right )\right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+6 x y \left (x \right ) = \sin \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+x y \left (x \right ) = \sqrt {x}\, \sin \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}-y \left (x \right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = x^{2} {\mathrm e}^{-x^{2}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1+\left (y \left (x \right )-x \right )^{2} \] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x -y \left (x \right )}{x +y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-\frac {y \left (x \right )}{x} = \frac {1}{y \left (x \right )} \] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+4 y \left (t \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-2 y \left (t \right ) = t^{3} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+3 y \left (t \right ) = \operatorname {Heaviside}\left (t -4\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \operatorname {Heaviside}\left (t -3\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \operatorname {Heaviside}\left (t -3\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[
{}y^{\prime }\left (t \right ) = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1 |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = 3 \delta \left (t -2\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \delta \left (t -2\right )-\delta \left (t -4\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = 4 \delta \left (-1+t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+3 y \left (t \right ) = \delta \left (t -2\right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = 0 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 4 x^{3}-x +2 \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sin \left (2 t \right )-\cos \left (2 t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\ln \left (x \right )}{x} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \sin \left (x \right )^{4} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+2 y \left (x \right ) = x^{2} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \cos \left (x \right )^{2} \sin \left (x \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+t^{2} = y \left (t \right )^{2} \] |
[_Riccati] |
✗ |
N/A |
|
|
\[ {}y^{\prime }\left (t \right ) = 4 t^{2}-t y \left (t \right )^{2} \] |
[_Riccati] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right ) \sqrt {t} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \tan \left (t \right ) y \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {1}{t^{2}+1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sqrt {y \left (t \right )^{2}-1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sqrt {25-y \left (t \right )^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right )+y \left (t \right ) = t^{3} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}t^{3} y^{\prime }\left (t \right )+t^{4} y \left (t \right ) = 2 t^{3} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime }\left (t \right )+t y \left (t \right ) = \ln \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) \sec \left (t \right ) = t \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+\frac {y \left (t \right )}{t -3} = \frac {1}{-1+t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (t -2\right ) y^{\prime }\left (t \right )+\left (t^{2}-4\right ) y \left (t \right ) = \frac {1}{2+t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+\frac {y \left (t \right )}{\sqrt {-t^{2}+4}} = t \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right )+y \left (t \right ) = t \sin \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+\tan \left (t \right ) y \left (t \right ) = \sin \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t y \left (t \right )^{2} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -\frac {t}{y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = -y \left (t \right )^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{3} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \cos \left (t \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}1 = \cos \left (y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\sin \left (y \right )^{2} = \frac {d}{d y}x \left (y \right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {\sqrt {t}}{y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sqrt {\frac {y \left (t \right )}{t}} \] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {{\mathrm e}^{t}}{y \left (t \right )+1} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = {\mathrm e}^{t -y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{\ln \left (y \left (x \right )\right )} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t \sin \left (t^{2}\right ) \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {1}{x^{2}+1} \] |
[_quadrature] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\sin \left (x \right )}{\cos \left (y \left (x \right )\right )+1} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {3+y \left (x \right )}{1+3 x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{x -y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = {\mathrm e}^{2 x -y \left (x \right )} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {3 y \left (x \right )+1}{x +3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \cos \left (t \right ) y \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{2} \cos \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \sqrt {y \left (t \right )}\, \cos \left (t \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {y \left (x \right )-2}{-2+x} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = 4 \,{\mathrm e}^{t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+3 t^{2} y \left (t \right ) = {\mathrm e}^{-t^{3}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+2 t y \left (t \right ) = 2 t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right )+y \left (t \right ) = 2 t \,{\mathrm e}^{t} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+4\right ) y^{\prime }\left (t \right )+2 t y \left (t \right ) = 2 t \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right ) = x \left (t \right )+t +1 \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = {\mathrm e}^{2 t}+2 y \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+\frac {y \left (t \right )}{2} = \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-\frac {y \left (t \right )}{2} = \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = t \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
|
||||
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 t y \left (t \right )^{2}+2 t^{2} y \left (t \right ) y^{\prime }\left (t \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}1+\frac {y \left (t \right )}{t^{2}}-\frac {y^{\prime }\left (t \right )}{t} = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 t y \left (t \right )+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }\left (t \right ) = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}y \left (t \right )^{2}-2 \sin \left (2 t \right )+\left (1+2 t y \left (t \right )\right ) y^{\prime }\left (t \right ) = 0 \] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
|
|
\[ {}\frac {2 t}{t^{2}+1}+y \left (t \right )+\left ({\mathrm e}^{y \left (t \right )}+t \right ) y^{\prime }\left (t \right ) = 0 \] |
[_exact] |
✗ |
N/A |
|
|
\[ {}2 y \left (t \right )+y^{\prime }\left (t \right ) = t^{2} \sqrt {y \left (t \right )} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-2 y \left (t \right ) = t^{2} \sqrt {y \left (t \right )} \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = \frac {4 y \left (t \right )^{2}-t^{2}}{2 t y \left (t \right )} \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}t +y \left (t \right )-t y^{\prime }\left (t \right ) = 0 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}t y^{\prime }\left (t \right )-y \left (t \right )-\sqrt {t^{2}+y \left (t \right )^{2}} = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}t^{3}+y \left (t \right )^{2} \sqrt {t^{2}+y \left (t \right )^{2}}-t y \left (t \right ) \sqrt {t^{2}+y \left (t \right )^{2}}\, y^{\prime }\left (t \right ) = 0 \] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
|
|
\[ {}y \left (t \right )^{3}-t^{3}-t y \left (t \right )^{2} y^{\prime }\left (t \right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
|
|
\[ {}t y \left (t \right )^{3}-\left (t^{4}+y \left (t \right )^{4}\right ) y^{\prime }\left (t \right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}y \left (t \right )^{4}+\left (t^{4}-t y \left (t \right )^{3}\right ) y^{\prime }\left (t \right ) = 0 \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
|
\[ {}2 x -y \left (x \right )-2+\left (-x +2 y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\sin \left (y \left (t \right )\right )-\cos \left (t \right ) y \left (t \right )+\left (t \cos \left (y \left (t \right )\right )-\sin \left (t \right )\right ) y^{\prime }\left (t \right ) = 0 \] |
[_exact] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = -x +y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right ) = t y \left (t \right )^{3} \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (2 t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{4 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}y^{\prime }\left (t \right )+4 y \left (t \right ) = {\mathrm e}^{-4 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x^{2}-y \left (x \right )^{2} \] |
[_Riccati] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +y \left (x \right )^{2} \] |
[[_Riccati, _special]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = x +y \left (x \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 2 y \left (x \right )-2 x^{2}-3 \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right ) = 2 x -y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\left (\frac {d}{d x}y \left (x \right )\right ) \sin \left (x \right )-y \left (x \right ) \cos \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}y \left (x \right ) \ln \left (y \left (x \right )\right )+x \left (\frac {d}{d x}y \left (x \right )\right ) = 1 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) \cos \left (y \left (x \right )\right )+1 = 0 \] |
[_separable] |
✓ |
✗ |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+\cos \left (2 y \left (x \right )\right ) = 1 \] |
[_separable] |
✓ |
✗ |
|
|
\[ {}x^{3} \left (\frac {d}{d x}y \left (x \right )\right )-\sin \left (y \left (x \right )\right ) = 1 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{2}-x \left (\frac {d}{d x}y \left (x \right )\right ) = y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\cos \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )-y \left (x \right ) \sin \left (x \right ) = 2 x \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-y \left (x \right ) \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}} \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )+y \left (x \right ) \cos \left (x \right ) = \cos \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\left (\frac {d}{d x}y \left (x \right )\right ) \sin \left (x \right )-y \left (x \right ) \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}} \] |
[_linear] |
✗ |
N/A |
|
|
\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right ) \cos \left (\frac {1}{x}\right )-y \left (x \right ) \sin \left (\frac {1}{x}\right ) = -1 \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}2 x \left (\frac {d}{d x}y \left (x \right )\right )-y \left (x \right ) = 1-\frac {2}{\sqrt {x}} \] |
[_linear] |
✗ |
N/A |
|
|
\[ {}2 x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = \left (x^{2}+1\right ) {\mathrm e}^{x} \] |
[_linear] |
✓ |
✗ |
|
|
\[ {}x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right ) = y \left (x \right )^{2} \ln \left (x \right ) \] |
[_Bernoulli] |
✓ |
✓ |
|
|
\[ {}x +y \left (x \right )+1+\left (2 x +2 y \left (x \right )-1\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = 1-x y \left (x \right ) \] |
[_linear] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )-x}{x +y \left (x \right )} \] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right ) \sin \left (x \right ) \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}\frac {d}{d x}y \left (x \right )-2 x y \left (x \right ) = 0 \] |
[_separable] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+3 x \left (t \right ) = {\mathrm e}^{-2 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )-3 x \left (t \right ) = 3 t^{3}+3 t^{2}+2 t +1 \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )-x \left (t \right ) = \cos \left (t \right )-\sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime }\left (t \right )+6 x \left (t \right ) = t \,{\mathrm e}^{-3 t} \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
\[ {}x^{\prime }\left (t \right )+x \left (t \right ) = 2 \sin \left (t \right ) \] |
[[_linear, ‘class A‘]] |
✓ |
✓ |
|
|
|
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|
|
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