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Mathematica |
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Sympy |
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 2 x^{2}
\]
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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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\[
{} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} 2 x^{2} y y^{\prime \prime }+4 y^{2} = x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }
\]
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\[
{} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\]
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\[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
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\[
{} 2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y = x^{2}
\]
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\[
{} 2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right )
\]
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\[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0
\]
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\[
{} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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\[
{} \left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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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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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\]
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\[
{} y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }}
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{4} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{3}
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime } = x^{2} y^{\prime }-y^{2}
\]
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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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\[
{} y^{\prime \prime } \sin \left (x \right )^{2} = 2 y
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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\[
{} \left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y = {\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x}
\]
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\[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2} = 0
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\]
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\[
{} x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\]
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\[
{} y^{\prime \prime } \cos \left (x \right )+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y = x^{2}
\]
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\[
{} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{x}
\]
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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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\[
{} y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y = \sin \left (x \right )^{2}
\]
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