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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-x y-x^{6}+64 = 0
\]
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\[
{} y^{\prime \prime }-x y-x = 0
\]
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\[
{} y^{\prime \prime }-x y-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y-x^{4} = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\]
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\[
{} y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\]
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\[
{} y^{\prime \prime }-x^{3} y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-x^{3} y-x^{4} = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\]
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\[
{} y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\]
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\[
{} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\]
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\[
{} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x
\]
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\[
{} 4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right )
\]
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\[
{} \frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}
\]
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\[
{} \frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )
\]
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\[
{} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\]
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\[
{} x y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}}
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{3}-x^{2}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
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\[
{} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\]
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\[
{} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{m +1}
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0
\]
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\[
{} y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x} = 0
\]
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\[
{} x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0
\]
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\[
{} x y^{\prime \prime }-x y^{\prime }-y-x \left (1+x \right ) {\mathrm e}^{x} = 0
\]
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\[
{} x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y-a \,x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-v^{2}+x^{2}\right ) y-f \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-\ln \left (x \right ) x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {d}{d x}\operatorname {LegendreP}\left (n , x\right ) = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0
\]
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\[
{} x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0
\]
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\[
{} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0
\]
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\[
{} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0
\]
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\[
{} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0
\]
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\[
{} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0
\]
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\[
{} y^{\prime \prime } = -\frac {\left (2 a x +b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (a v x -b \right ) y}{\left (a x +b \right ) x^{2}}+A x
\]
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\[
{} y^{\prime \prime } = -\frac {b y}{x^{2} \left (-a +x \right )^{2}}+c
\]
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\[
{} y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )}
\]
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\[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\]
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\[
{} x^{2} \left (-a +x \right )^{2} y^{\prime \prime }+b y = c \,x^{2} \left (-a +x \right )^{2}
\]
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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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\[
{} \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y = x
\]
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