2.883   ODE No. 883

$y'(x)=\frac {x \left (a^3 y(x)^6+a^3 y(x)^4+a^3+3 a^2 b x^2 y(x)^4+2 a^2 b x^2 y(x)^2+3 a b^2 x^4 y(x)^2+a b^2 x^4+b^3 x^6\right )}{a^{7/2} y(x)}$ Mathematica : cpu = 1.13492 (sec), leaf count = 164

$\text {Solve}\left [\frac {x^2}{2}-\frac {1}{2} a^{5/2} \text {RootSum}\left [\text {\#1}^3 b^3+3 \text {\#1}^2 a b^2 y(x)^2+\text {\#1}^2 a b^2+3 \text {\#1} a^2 b y(x)^4+2 \text {\#1} a^2 b y(x)^2+a^{5/2} b+a^3 y(x)^6+a^3 y(x)^4+a^3\& ,\frac {\log \left (x^2-\text {\#1}\right )}{3 \text {\#1}^2 b^2+6 \text {\#1} a b y(x)^2+2 \text {\#1} a b+3 a^2 y(x)^4+2 a^2 y(x)^2}\& \right ]=c_1,y(x)\right ]$ Maple : cpu = 0.511 (sec), leaf count = 352

$\left \{ \int _{{\it \_b}}^{x}\!{ \left ( {b}^{3}{{\it \_a}}^{6}+3\, \left ( y \left ( x \right ) \right ) ^{2}a{b}^{2}{{\it \_a}}^{4}+3\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}b{{\it \_a}}^{2}+ \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+a{{\it \_a}}^{4}{b}^{2}+2\,{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}b{{\it \_a}}^{2}+ \left ( y \left ( x \right ) \right ) ^{4}{a}^{3}+{a}^{3} \right ) {\it \_a} \left ( \left ( y \left ( x \right ) \right ) ^{6}{a}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}b{{\it \_a}}^{2}+3\, \left ( y \left ( x \right ) \right ) ^{2}a{b}^{2}{{\it \_a}}^{4}+{b}^{3}{{\it \_a}}^{6}+ \left ( y \left ( x \right ) \right ) ^{4}{a}^{3}+2\,{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}b{{\it \_a}}^{2}+a{{\it \_a}}^{4}{b}^{2}+{a}^{3}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}{a}^{-{\frac {7}{2}}}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{{\it \_f} \left ( {{\it \_f}}^{6}{a}^{3}+3\,{{\it \_f}}^{4}{a}^{2}b{x}^{2}+3\,{{\it \_f}}^{2}a{b}^{2}{x}^{4}+{b}^{3}{x}^{6}+{a}^{3}{{\it \_f}}^{4}+2\,{a}^{2}{{\it \_f}}^{2}b{x}^{2}+a{x}^{4}{b}^{2}+{a}^{3}+{a}^{{\frac {5}{2}}}b \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!6\,{\frac {{\it \_f}\,{\it \_a}\, \left ( b{{\it \_a}}^{2}+a{{\it \_f}}^{2} \right ) \left ( a{{\it \_f}}^{2}+b{{\it \_a}}^{2}+2/3\,a \right ) b}{ \left ( {a}^{5/2}b+ \left ( {{\it \_f}}^{6}+{{\it \_f}}^{4}+1 \right ) {a}^{3}+3\,{{\it \_f}}^{2}{{\it \_a}}^{2} \left ( {{\it \_f}}^{2}+2/3 \right ) b{a}^{2}+3\,{{\it \_a}}^{4} \left ( {{\it \_f}}^{2}+1/3 \right ) {b}^{2}a+{b}^{3}{{\it \_a}}^{6} \right ) ^{2}}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \}$