#### 2.147   ODE No. 147

$a x^2 y(x)^3+b y(x)^2+x^2 y'(x)=0$ Mathematica : cpu = 0.634131 (sec), leaf count = 343

$\text {Solve}\left [\frac {\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Ai}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\text {Ai}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}{\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Bi}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\text {Bi}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}+c_1=0,y(x)\right ]$ Maple : cpu = 0.16 (sec), leaf count = 178

$\left \{ y \left ( x \right ) =-{\sqrt [3]{2}abx \left ( \sqrt [3]{2}a{b}^{2}-2\, \left ( {a}^{2}{b}^{2} \right ) ^{2/3}{\it RootOf} \left ( {{\rm Bi}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )}{\it \_C1}\,{\it \_Z}+{\it \_Z}\,{{\rm Ai}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )}+{{\rm Bi}^{(1)}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )}{\it \_C1}+{{\rm Ai}^{(1)}\left (-1/2\,{\frac {a{2}^{2/3}x-2\,{{\it \_Z}}^{2}\sqrt [3]{{a}^{2}{b}^{2}}}{\sqrt [3]{{a}^{2}{b}^{2}}}}\right )} \right ) x \right ) ^{-1}} \right \}$