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Mathematica |
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right )
\]
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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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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x}
\]
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\[
{} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right )
\]
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\[
{} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x}
\]
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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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\[
{} y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x}
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3}
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}}
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right )
\]
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\[
{} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right )
\]
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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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\[
{} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\]
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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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\[
{} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0
\]
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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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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8
\]
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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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\[
{} y^{\prime \prime \prime \prime }-16 y = 0
\]
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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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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x}
\]
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\[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right )
\]
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\[
{} x y^{\prime \prime }-y^{\prime } = -3 x {y^{\prime }}^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1}
\]
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\[
{} 4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}}
\]
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