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Mathematica |
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\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2}
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
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\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
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\[
{}y^{\prime \prime }-36 y = 0
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 4 x^{2}+5
\] |
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\[
{}y^{\prime \prime }+y = 6 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-y = 9 \,{\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 4 \cos \left (x \right )-2 \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }+y = 3 \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \sin \left (x \right ) {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}}
\] |
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\[
{}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3}
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1}
\] |
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\[
{}y^{\prime \prime }-4 y = \frac {8}{1+{\mathrm e}^{2 x}}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}}
\] |
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\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2}
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1
\] |
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\[
{}y^{\prime \prime }-y = 2 \tanh \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-9 y = F \left (x \right )
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = F \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 5 \,{\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )}
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k}
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
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\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
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\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \left (x \right )
\] |
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\[
{}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-12 y = 36
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t}
\] |
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