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Mathematica |
Maple |
Sympy |
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\[
{} y y^{\prime \prime } = 6 x^{4}
\]
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\[
{} [x^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right )]
\]
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\[
{} y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\]
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\[
{} y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{x +{\mathrm e}^{y}}
\]
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\[
{} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\]
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\[
{} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\]
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\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\]
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\[
{} y^{\prime } = \frac {x^{2}+y^{2}}{\sin \left (x \right )}
\]
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\[
{} y^{\prime } = \frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}}
\]
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\[
{} y^{\prime } = \frac {x^{2}+y^{2}}{\ln \left (x y\right )}
\]
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\[
{} y^{\prime } = \left (x^{2}+y^{2}\right ) y^{{1}/{3}}
\]
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\[
{} y^{\prime } = \ln \left (1+x^{2}+y^{2}\right )
\]
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\[
{} y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
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\[
{} y^{\prime } = \left (x^{2}+y^{2}\right )^{2}
\]
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\[
{} 2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime } = 0
\]
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\[
{} y \sin \left (x y\right )+x y^{2} \cos \left (x y\right )+\left (x \sin \left (x y\right )+x y^{2} \cos \left (x y\right )\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} \cos \left (x \right ) y-x^{3} y \sin \left (x \right )+4 x +\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = y^{2}+\cos \left (t^{2}\right )
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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\[
{} y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\]
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\[
{} y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\]
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\[
{} y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\]
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\[
{} 2 t \cos \left (y\right )+3 t^{2} y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\]
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\[
{} y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\]
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\[
{} y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\]
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\[
{} y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\]
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\[
{} y^{\prime } = y+{\mathrm e}^{-y}+2 t
\]
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\[
{} y^{\prime } = \frac {t^{2}+y^{2}}{1+t +y^{2}}
\]
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\[
{} y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 y \left (t \right )^{2}-3 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -b x \left (t \right ) y \left (t \right )+m, y^{\prime }\left (t \right ) = b x \left (t \right ) y \left (t \right )-g y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right ), z^{\prime }\left (t \right ) = x \left (t \right )+\sin \left (z \left (t \right )\right )]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {\left (x_{1} \left (t \right )^{2}+\sqrt {x_{1} \left (t \right )^{2}+4 x_{2} \left (t \right )^{2}}\right ) x_{1} \left (t \right )}{2}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4}]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}+1, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = \tan \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right )+x \left (t \right )^{3}]
\]
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\[
{} x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0
\]
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\[
{} y-x^{2} \sqrt {-y^{2}+x^{2}}-x y^{\prime } = 0
\]
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\[
{} y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\]
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\[
{} 1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2} = 0
\]
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\[
{} x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime } = y
\]
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\[
{} y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\]
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\[
{} y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-t \cos \left (t \right )\right ]
\]
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\[
{} y^{2} \left (x^{2}+1\right )+y+\left (1+2 x y\right ) y^{\prime } = 0
\]
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\[
{} 2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\]
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\[
{} x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = f \left (x \right )+a y+b y^{2}
\]
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\[
{} y^{\prime } = f \left (x \right )+g \left (x \right ) y+a y^{2}
\]
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\[
{} y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2}
\]
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\[
{} y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\]
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\[
{} y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n}
\]
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\[
{} y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\]
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\[
{} y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0
\]
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\[
{} y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0
\]
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\[
{} x y^{\prime } = \sin \left (x -y\right )
\]
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\[
{} x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\]
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\[
{} y y^{\prime }+x^{3}+y = 0
\]
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\[
{} y y^{\prime }+f \left (x \right ) = g \left (x \right ) y
\]
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\[
{} \left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0
\]
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\[
{} x \left (a +y\right ) y^{\prime }+b x +c y = 0
\]
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\[
{} \left (a +x \left (x +y\right )\right ) y^{\prime } = b \left (x +y\right ) y
\]
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\[
{} \left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\]
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\[
{} {y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right )
\]
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\[
{} x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0
\]
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\[
{} \left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\]
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\[
{} x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\]
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\[
{} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\]
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\[
{} \frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0
\]
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\[
{} s^{2}+s^{\prime } = \frac {s+1}{s t}
\]
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\[
{} x^{\prime }+t x = {\mathrm e}^{x}
\]
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\[
{} x x^{\prime }+x t^{2} = \sin \left (t \right )
\]
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\[
{} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\]
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\[
{} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\]
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\[
{} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\]
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\[
{} \sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime } = 6 \sqrt {y}+5 x^{3}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 y^{\prime } x^{2}+8 x^{3} y = 0
\]
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\[
{} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
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\[
{} [y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right ) x -y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )]
\]
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\[
{} 2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 1+t y \left (t \right ), y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\]
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\[
{} y^{\prime } = y+x \,{\mathrm e}^{y}
\]
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