2.40   ODE No. 40

\[ 3 a y(x)^3+6 a x y(x)^2+y'(x)=0 \]

✓ Mathematica : cpu = 0.34965 (sec), leaf count = 185

DSolve[6*a*x*y[x]^2 + 3*a*y[x]^3 + Derivative[1][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.046 (sec), leaf count = 48

dsolve(diff(y(x),x)+3*a*y(x)^3+6*a*x*y(x)^2 = 0,y(x))
 

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