#### 2.145   ODE No. 145

$-a x^2 y(x)^2+a y(x)^3+x^2 y'(x)=0$ Mathematica : cpu = 0.476071 (sec), leaf count = 267

$\text {Solve}\left [\frac {\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \text {Ai}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\text {Ai}'\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}{\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \text {Bi}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\text {Bi}'\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}+c_1=0,y(x)\right ]$ Maple : cpu = 0.085 (sec), leaf count = 117

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