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\[
{} y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+c \left ({\mathrm e}^{\lambda x} a +b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-\lambda b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 x \mu }+c \,{\mathrm e}^{x \mu }+k \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 x \mu }+d \,{\mathrm e}^{x \mu }+k \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{x \mu }+\lambda \right ) y = 0
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b \,{\mathrm e}^{x \mu }-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+c \,{\mathrm e}^{2 \lambda x}+b^{2} {\mathrm e}^{2 x \mu }+b \left (\mu -\lambda \right ) {\mathrm e}^{x \mu }\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{x \left (\lambda +\mu \right )}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{x \mu }-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y = 0
\]
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\[
{} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y = 0
\]
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\[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y = 0
\]
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\[
{} \left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y = 0
\]
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\[
{} 2 \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y = 0
\]
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\[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y = 0
\]
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\[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y = 0
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+25 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 1+{\mathrm e}^{2 x}
\]
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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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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime } x^{2}+x y = x
\]
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\[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right ) = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x} = {\mathrm e}^{4 x}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2} = 0
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\]
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\[
{} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
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\[
{} x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\]
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\[
{} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2\right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0
\]
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\[
{} \left (2 x^{3}-1\right ) y^{\prime \prime }-6 y^{\prime } x^{2}+6 x y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\]
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\[
{} x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime } = x
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{x} x
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\]
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\[
{} \left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\]
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\[
{} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0
\]
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\[
{} x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+2 x = 0
\]
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\[
{} t^{2} x^{\prime \prime }-6 x = 0
\]
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\[
{} 2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\]
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\[
{} x^{\prime \prime } = -3 \sqrt {t}
\]
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\[
{} x^{\prime }+t x^{\prime \prime } = 1
\]
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\[
{} \frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\]
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\[
{} x^{\prime \prime }+x^{\prime } = 3 t
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime } = 0
\]
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\[
{} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+3 x = 0
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime } = 0
\]
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\[
{} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+3 x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+6 x = 0
\]
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\[
{} x^{\prime \prime }+9 x = 0
\]
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\[
{} x^{\prime \prime }-12 x = 0
\]
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\[
{} 2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\]
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