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Mathematica |
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\]
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\[
{} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1
\]
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\[
{} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 8 \sin \left (t \right ) {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime }-2 k y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+20 y = 0
\]
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\[
{} y^{\prime \prime } = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+20 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = x^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime } = x^{2}+2 x
\]
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\[
{} y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+9 y = 8 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \cot \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right )
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\]
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\[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x}
\]
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\[
{} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} y^{3} y^{\prime \prime } = k
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}-1
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
\]
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\[
{} x y^{\prime \prime }-y^{\prime } = x^{2}
\]
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\[
{} \left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\]
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\[
{} r^{\prime \prime } = -\frac {k}{r^{2}}
\]
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\[
{} y^{\prime \prime } = \frac {3 k y^{2}}{2}
\]
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\[
{} y^{\prime \prime } = 2 k y^{3}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
\]
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\[
{} r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0
\]
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\[
{} \left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} 2 y^{\prime \prime } = {\mathrm e}^{y}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
\]
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\[
{} x y^{\prime \prime }-y^{\prime } = x^{2}
\]
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