2.145   ODE No. 145

\[ -a x^2 y(x)^2+a y(x)^3+x^2 y'(x)=0 \]

✓ Mathematica : cpu = 0.54507 (sec), leaf count = 267

DSolve[-(a*x^2*y[x]^2) + a*y[x]^3 + x^2*Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\frac {\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \text {Ai}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\text {Ai}'\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}{\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \text {Bi}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\text {Bi}'\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}+c_1=0,y(x)\right ]\]

✓ Maple : cpu = 0.125 (sec), leaf count = 117

dsolve(x^2*diff(y(x),x)+a*y(x)^3-a*x^2*y(x)^2 = 0,y(x))
 

\[y \left (x \right ) = -\frac {1}{a x +\left (-2 a \right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {\textit {\_Z}^{2} \left (-2 a \right )^{{1}/{3}} x -1}{\left (-2 a \right )^{{1}/{3}} x}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {\textit {\_Z}^{2} \left (-2 a \right )^{{1}/{3}} x -1}{\left (-2 a \right )^{{1}/{3}} x}\right )+\operatorname {AiryBi}\left (1, \frac {\textit {\_Z}^{2} \left (-2 a \right )^{{1}/{3}} x -1}{\left (-2 a \right )^{{1}/{3}} x}\right ) c_{1} +\operatorname {AiryAi}\left (1, \frac {\textit {\_Z}^{2} \left (-2 a \right )^{{1}/{3}} x -1}{\left (-2 a \right )^{{1}/{3}} x}\right )\right )}\]