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Mathematica |
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\[
{}y^{\prime \prime }-f \left (y^{\prime }, a x +b y\right ) = 0
\] |
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\[
{}y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right ) = 0
\] |
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\[
{}y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{1-n}\right ) = 0
\] |
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\[
{}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0
\] |
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\[
{}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\] |
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\[
{}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\] |
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\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\] |
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\[
{}x y^{\prime \prime }+\left (y-1\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\] |
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\[
{}x y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b = 0
\] |
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\[
{}2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\] |
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\[
{}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (a +1\right ) x y^{\prime }-x^{k} f \left (x^{k} y, x y^{\prime }+k y\right ) = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b \,x^{2} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\] |
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\[
{}9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0
\] |
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\[
{}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0
\] |
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\[
{}x^{3} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\] |
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\[
{}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\] |
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\[
{}x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0
\] |
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\[
{}x^{4} y^{\prime \prime }-x^{2} \left (x +y^{\prime }\right ) y^{\prime }+4 y^{2} = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{3} = 0
\] |
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\[
{}y^{\prime \prime } \sqrt {x}-y^{{3}/{2}} = 0
\] |
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\[
{}\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right ) = 0
\] |
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\[
{}x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}} = 0
\] |
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\[
{}f \left (x \right )^{2} y^{\prime \prime }+f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }-h \left (y, f \left (x \right ) y^{\prime }\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-a = 0
\] |
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\[
{}y y^{\prime \prime }-a x = 0
\] |
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\[
{}y y^{\prime \prime }-a \,x^{2} = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0
\] |
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\[
{}y y^{\prime \prime }+y^{2}-a x -b = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime }+f \left (x \right ) y^{3}+y^{2} \left (\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 y^{2} a +b y^{3} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 y^{3} b^{2}+a y = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (y^{2} b^{2}-a^{2}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+y^{2} f \left (x \right )\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-a {y^{\prime }}^{2} = 0
\] |
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\[
{}y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{3} = 0
\] |
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\[
{}y y^{\prime \prime }+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a} = 0
\] |
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\[
{}y y^{\prime \prime }+a {y^{\prime }}^{2}+f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2} = 0
\] |
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\[
{}y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0
\] |
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\[
{}y y^{\prime \prime }-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (2+a \right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{2+a} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
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\[
{}y^{\prime \prime } \left (x +y\right )+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right ) = 0
\] |
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\[
{}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
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\[
{}y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right ) = 0
\] |
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\[
{}2 y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 \left (x +2 y\right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}-3 y^{4} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+3 f \left (x \right ) y y^{\prime }+2 \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y^{2}-8 y^{3} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+4 y^{\prime } y^{2}+1+y^{2} f \left (x \right )+y^{4} = 0
\] |
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\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2}-4 y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+y^{2} f \left (x \right ) = 0
\] |
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\[
{}2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
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\[
{}2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\] |
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\[
{}3 y y^{\prime \prime }-5 {y^{\prime }}^{2} = 0
\] |
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\[
{}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y = 0
\] |
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\[
{}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3} = 0
\] |
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\[
{}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0
\] |
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\[
{}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+\left (6 y^{2}-\frac {2 f^{\prime }\left (x \right ) y}{f \left (x \right )}\right ) y^{\prime }+y^{4}-2 y^{\prime } y^{2}+g \left (x \right ) y^{2}+f \left (x \right ) y = 0
\] |
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\[
{}4 y y^{\prime \prime }-5 {y^{\prime }}^{2}+y^{2} a = 0
\] |
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\[
{}12 y y^{\prime \prime }-15 {y^{\prime }}^{2}+8 y^{3} = 0
\] |
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\[
{}n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0
\] |
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\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}} = 0
\] |
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\[
{}a y y^{\prime \prime }-\left (a -1\right ) {y^{\prime }}^{2}+\left (2+a \right ) f \left (x \right ) y^{2} y^{\prime }+f \left (x \right )^{2} y^{4}+a f^{\prime }\left (x \right ) y^{3} = 0
\] |
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