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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} y \left (1+y^{2}\right ) y^{\prime \prime }+\left (1-3 y^{2}\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\]
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\[
{} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\]
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\[
{} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\]
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\[
{} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} \left (-1+y^{2}\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2} = 0
\]
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\[
{} \left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y = 0
\]
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\[
{} \sqrt {y}\, y^{\prime \prime }-a = 0
\]
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\[
{} \sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\]
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\[
{} h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\]
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\[
{} y^{\prime \prime } y^{\prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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\[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
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\[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\]
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\[
{} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\]
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\[
{} \left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{3} y+3 x y^{\prime }+y = 0
\]
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\[
{} \left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }+y^{3} = 0
\]
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\[
{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0
\]
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\[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
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\[
{} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x y^{\prime \prime } \left (x +4 y^{\prime }\right )+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\]
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\[
{} 3 x^{2} {y^{\prime \prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (1-6 x \right ) y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 {y^{\prime }}^{2} x = 0
\]
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\[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
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\[
{} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\]
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\[
{} \left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0
\]
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\[
{} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }-f \left (y\right ) = 0
\]
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\[
{} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\]
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\[
{} y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\]
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\[
{} y^{\prime \prime }+a y = 0
\]
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\[
{} y^{\prime \prime }-\left (a x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\]
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\[
{} y^{\prime \prime }-\left (a \,x^{2}+b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\]
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\[
{} y^{\prime \prime }-\left (a \,x^{2}+b x c \right ) y = 0
\]
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\[
{} y^{\prime \prime }-a \,x^{n} y = 0
\]
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\[
{} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\]
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\[
{} y^{\prime \prime }-2 x y^{\prime }+2 n y = 0
\]
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\[
{} y^{\prime \prime }+a x y^{\prime }+b y = 0
\]
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\[
{} y^{\prime \prime }+a x y^{\prime }+b x y = 0
\]
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\[
{} y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 a x y^{\prime }+\left (x^{4} b +a^{2} x^{2}+c x +a \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a \,x^{3} b +a c \,x^{2}+b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a \,x^{3} b -a \,x^{2}+b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{3} b +b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y = 0
\]
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\[
{} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{m +n}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (1+m \right ) x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{m +n}+b \left (1+m \right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{m +n}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b x y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+n y^{\prime }+b \,x^{-2 n +1} y = 0
\]
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\[
{} x y^{\prime \prime }+\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y = 0
\]
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