#### 2.741   ODE No. 741

$y'(x)=\frac {x \left (a y(x)^2+b x^2\right )^3}{a^{5/2} y(x) \left (a y(x)^2+a+b x^2\right )}$ Mathematica : cpu = 2.10914 (sec), leaf count = 175

$\text {Solve}\left [\frac {1}{2} \left (x^2-a^{3/2} \text {RootSum}\left [3 \text {\#1}^2 a b^2 y(x)^2+\text {\#1}^3 b^3+\text {\#1} a^{3/2} b^2+3 \text {\#1} a^2 b y(x)^4+a^{5/2} b y(x)^2+a^{5/2} b+a^3 y(x)^6\& ,\frac {a y(x)^2 \log \left (x^2-\text {\#1}\right )+a \log \left (x^2-\text {\#1}\right )+\text {\#1} b \log \left (x^2-\text {\#1}\right )}{3 \text {\#1}^2 b^2+6 \text {\#1} a b y(x)^2+a^{3/2} b+3 a^2 y(x)^4}\& \right ]\right )=c_1,y(x)\right ]$ Maple : cpu = 1.548 (sec), leaf count = 246

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