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\[
{} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\]
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\[
{} x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime } = y+x^{2}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+y = 0
\]
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\[
{} 2 y^{\prime \prime }-3 y^{\prime }-2 y = 0
\]
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\[
{} \left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\]
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\[
{} x y^{\prime \prime }+2 x^{2} y^{\prime }+\sin \left (x \right ) y = \sinh \left (x \right )
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\]
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\[
{} y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y = \tan \left (x \right )
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
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\[
{} x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x
\]
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\[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x
\]
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\[
{} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\]
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\[
{} x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\]
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\[
{} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right )
\]
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\[
{} x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1
\]
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\[
{} y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0
\]
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\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (x +2\right ) y}{x^{2} \left (1+x \right )} = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0
\]
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\[
{} \frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (3 x +1\right ) y^{\prime }}{x}+\frac {y}{x} = 3 x
\]
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\[
{} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\]
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\[
{} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+9 y = 0
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 0
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+37 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
\]
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\[
{} 4 y^{\prime \prime }-12 y^{\prime }+13 y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-20 y^{\prime }+51 y = 0
\]
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\[
{} 2 y^{\prime \prime }+3 y^{\prime }+y = 0
\]
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\[
{} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 0
\]
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\[
{} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\]
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\[
{} 4 y^{\prime \prime }+40 y^{\prime }+101 y = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+34 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+3 y = 9 t
\]
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\[
{} 4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1
\]
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\[
{} 4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }+9 y = {\mathrm e}^{-2 t}
\]
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\[
{} 2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = t +2
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right )
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = t^{2}
\]
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\[
{} 2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right )
\]
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\[
{} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right )
\]
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\[
{} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right )
\]
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\[
{} 4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right )
\]
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\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7}
\]
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\[
{} t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t
\]
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\[
{} y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\]
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\[
{} t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 1
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-7 y = 4
\]
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\[
{} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2}
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{{3}/{2}} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+4 y = 2 \sec \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\]
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\[
{} y^{\prime \prime }+y = f \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y = 0
\]
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