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ODE |
Mathematica |
Maple |
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{x \mu }+\lambda \right ) y = 0
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} c a +b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} \frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0
\]
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\[
{} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\]
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\[
{} x \,{\mathrm e}^{\frac {y}{x}}+y-x y^{\prime } = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime }-2 \left (1+x \right ) y = y^{{5}/{2}}
\]
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\[
{} x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0
\]
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\[
{} \frac {x y^{\prime }-y}{\sqrt {x^{2}-y^{2}}} = x y^{\prime }
\]
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\[
{} x y^{\prime }-a y+b y^{2} = c \,x^{2 a}
\]
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\[
{} x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\]
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\[
{} 5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right ) = \left (x^{2}+y^{2}+x \right ) \left (x y^{\prime }-y\right )
\]
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\[
{} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-x y^{\prime }\right ) = 0
\]
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\[
{} x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
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\[
{} a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} \left (x y^{\prime }-y\right )^{2} = 1+{y^{\prime }}^{2}
\]
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\[
{} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0
\]
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\[
{} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0
\]
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\[
{} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\]
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\[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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\[
{} a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
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\[
{} \left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right )
\]
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\[
{} y y^{\prime } = \left (x -b \right ) {y^{\prime }}^{2}+a
\]
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\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = a^{2} y^{\prime }
\]
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\[
{} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\]
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\[
{} y = x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}}
\]
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\[
{} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = x^{2} y^{2}+x^{4}
\]
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\[
{} y = x y^{\prime }+\frac {1}{y^{\prime }}
\]
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\[
{} 8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y = x
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\]
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\[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+{\mathrm e}^{2 x} y = {\mathrm e}^{4 x}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\]
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\[
{} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
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\[
{} x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\]
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\[
{} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\]
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\[
{} x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\]
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\[
{} \left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2} = {y^{\prime \prime \prime }}^{2}+1
\]
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\[
{} \left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
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\[
{} x y^{\prime \prime \prime }-y^{\prime \prime }-x y^{\prime }+y = -x^{2}+1
\]
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\[
{} \left (x +2\right )^{2} y^{\prime \prime \prime }+\left (x +2\right ) y^{\prime \prime }+y^{\prime } = 1
\]
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\[
{} \left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\]
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\[
{} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0
\]
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\[
{} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0
\]
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\[
{} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0
\]
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\[
{} x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0
\]
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\[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} x^{3} y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2}
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
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\[
{} \left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} x \left (x +2 y\right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\]
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\[
{} x^{\prime } = x^{2}+t^{2}
\]
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\[
{} x^{\prime } = \sqrt {x}
\]
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\[
{} T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\]
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\[
{} y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\]
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\[
{} x^{\prime } = t -x^{2}
\]
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\[
{} x x^{\prime } = 1-t x
\]
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\[
{} {x^{\prime }}^{2}+t x = \sqrt {t +1}
\]
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\[
{} t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\]
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\[
{} x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\]
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\[
{} x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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