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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 1
\]
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\[
{} y^{\prime \prime }-4 y^{\prime } = 5
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
\]
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\[
{} y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right )
\]
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\[
{} y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\]
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\[
{} y^{\prime \prime }+2 y = 2+{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right )
\]
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\[
{} y^{\prime \prime }-y = x^{2}
\]
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\[
{} y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}}
\]
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\[
{} y^{\prime \prime }-y = x \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +\ln \left (x \right ) x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2
\]
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\[
{} \left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8
\]
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\[
{} \left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
\]
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\[
{} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\]
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\[
{} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x}
\]
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\[
{} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\]
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\[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y = x
\]
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\[
{} x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
\]
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\[
{} \left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+4 x y = 4
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x}
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}}
\]
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\[
{} x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right )
\]
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\[
{} \left (x +2 y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+6 y = 10
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime } = f \left (x \right )
\]
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\[
{} y^{\prime \prime }+9 y = 18
\]
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\[
{} y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }+y = {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }+9 y = 5
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8
\]
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\[
{} y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\]
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\[
{} y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\]
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\[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\]
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\[
{} 4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1
\]
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\[
{} x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
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\[
{} x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right )
\]
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\[
{} x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\]
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\[
{} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = x^{2}-1
\]
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\[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x}
\]
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\[
{} x^{2} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2}
\]
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