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ODE |
Mathematica |
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\]
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\[
{} y^{\prime \prime }-y a^{2} = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\]
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\[
{} y^{\prime \prime }+y a^{2} = \sec \left (a x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-9 y^{\prime }+20 y = 20 x
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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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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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\]
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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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\[
{} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\]
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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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\[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
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\[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
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\[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
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\[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} a^{2} y^{\prime \prime } y^{\prime } = x
\]
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\[
{} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
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\[
{} y^{\prime \prime } = \frac {a}{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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\[
{} y^{3} y^{\prime \prime } = a
\]
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\[
{} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2}
\]
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\[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y^{\prime } x^{2}+x y = x
\]
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\[
{} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y a^{2} = \frac {1}{x^{2}}
\]
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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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\[
{} y^{\prime \prime }+x y^{\prime }-y = f \left (x \right )
\]
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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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\[
{} y y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }-y = 5 x +2
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x}
\]
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\[
{} y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y a^{2} = \cos \left (a x \right )+\cos \left (b x \right )
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
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\[
{} y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = \cosh \left (x \right ) \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime } = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = x
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = x^{2} \sin \left (\ln \left (x \right )\right )
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime } = \left (2 x +3\right ) \left (2 x +4\right )
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right ) = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 x
\]
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\[
{} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
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\[
{} y^{\prime \prime } = x +\sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{x} x
\]
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\[
{} \cos \left (x \right )^{2} y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime } = \frac {a}{x}
\]
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\[
{} y^{\prime \prime } \sqrt {a^{2}+x^{2}} = x
\]
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\[
{} x^{2} y^{\prime \prime } = \ln \left (x \right )
\]
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\[
{} y^{3} y^{\prime \prime } = a
\]
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