2.147 ODE No. 147
\[ a x^2 y(x)^3+b y(x)^2+x^2 y'(x)=0 \]
✓ Mathematica : cpu = 0.695751 (sec), leaf count = 343
DSolve[b*y[x]^2 + a*x^2*y[x]^3 + x^2*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Ai}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\text {Ai}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}{\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Bi}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\text {Bi}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}+c_1=0,y(x)\right ]\]
✓ Maple : cpu = 0.337 (sec), leaf count = 182
dsolve(x^2*diff(y(x),x)+a*x^2*y(x)^3+b*y(x)^2 = 0,y(x))
\[y \left (x \right ) = -\frac {2^{{1}/{3}} a b x}{2^{{1}/{3}} a \,b^{2}-2 \left (a^{2} b^{2}\right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {-a 2^{{2}/{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {-a 2^{{2}/{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )+\operatorname {AiryBi}\left (1, \frac {-a 2^{{2}/{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_{1} +\operatorname {AiryAi}\left (1, \frac {-a 2^{{2}/{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )\right ) x}\]