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Mathematica |
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\[
{}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x}
\] |
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\[
{}y^{\prime \prime }+9 y = 39 \,{\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime } = 20
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime } = x^{2}
\] |
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\[
{}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x}
\] |
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\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x}
\] |
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\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right ) {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right ) {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 100
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8
\] |
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\[
{}y^{\prime \prime }+9 y = \sin \left (x \right ) {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (2 x \right ) x^{2}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x}
\] |
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\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}}
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}}
\] |
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\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )
\] |
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\[
{}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3}
\] |
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\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x}
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 \ln \left (x \right ) x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 \sqrt {x}
\] |
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\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \csc \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-2 y = \frac {1}{x -2}
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
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\[
{}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+36 y = 0
\] |
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\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
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\[
{}y^{\prime \prime }-36 y = 0
\] |
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\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0
\] |
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\[
{}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x}
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
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\[
{}y^{\prime \prime }+3 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-6 y = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
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\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
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\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-30 y = 0
\] |
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\[
{}16 y^{\prime \prime }-8 y^{\prime }+y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
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\[
{}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
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\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 = 0
\] |
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\[
{}y^{\prime \prime }+20 y^{\prime }+100 y = 0
\] |
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\[
{}x y^{\prime \prime } = 3 y^{\prime }
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2}
\] |
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\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x}
\] |
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\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}
\] |
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\[
{}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right )
\] |
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