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ODE |
Mathematica |
Maple |
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\[
{} 1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\]
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\[
{} x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\]
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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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\[
{} \left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\]
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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\]
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\[
{} {y^{\prime }}^{2}+y^{2} = 1
\]
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\[
{} \left (2 x y^{\prime }-y\right )^{2} = 8 x^{3}
\]
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\[
{} \left (x^{2}+1\right ) {y^{\prime }}^{2} = 1
\]
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\[
{} {y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (-y^{2}+x^{2}\right ) y^{2} = 0
\]
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\[
{} 2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0
\]
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\[
{} 4 {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\]
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\[
{} y^{\prime }+2 x y = x^{2}+y^{2}
\]
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\[
{} y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\]
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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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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\]
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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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\[
{} \left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2} = 0
\]
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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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\[
{} \left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-y^{\prime } x^{2}\right )
\]
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\[
{} y^{2} \left (1+{y^{\prime }}^{2}\right ) = a^{2}
\]
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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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\[
{} 3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0
\]
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\[
{} y = \left (1+x \right ) {y^{\prime }}^{2}
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right ) = a^{2} y^{\prime }
\]
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\[
{} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2}
\]
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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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\[
{} x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\]
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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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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2} = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2} = 0
\]
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\[
{} 8 \left (y^{\prime }+1\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}
\]
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\[
{} 4 {y^{\prime }}^{2} = 9 x
\]
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\[
{} y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+25 y = 0
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime } = 0
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\]
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\[
{} 4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-y = x^{2}
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime } = 3 x^{2}+\sin \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = {\mathrm e}^{x}+4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 1+{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = \cos \left (x \right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = x \ln \left (x \right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x}
\]
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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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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime } = x^{2}-3 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\]
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\[
{} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2}
\]
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\[
{} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{2}-x
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+y = x \cos \left (x \right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime \prime }-y = {\mathrm e}^{x} x +\cos \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-y^{\prime } x^{2}+x y = x
\]
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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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\[
{} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right ) = {\mathrm e}^{x}
\]
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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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