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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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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x}
\]
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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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\[
{} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right )
\]
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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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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime }-4 y = t^{3}
\]
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\[
{} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 7
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} t y^{\prime \prime }+y^{\prime }+t y = 0
\]
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\[
{} y^{\prime \prime }-9 y = 0
\]
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\[
{} y^{\prime \prime }+9 y = 27 t^{3}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+17 y = 0
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+13 y = 0
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+17 y = 0
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 1
\]
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\[
{} y^{\prime \prime }+4 y = t
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 1
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\]
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\[
{} y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime } = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right )
\]
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