2.1819   ODE No. 1819

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

✗ Mathematica : cpu = 1.44393 (sec), leaf count = 0

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

, could not solve

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

✓ Maple : cpu = 0.065 (sec), leaf count = 42

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

\[y \left (x \right ) = {\mathrm e}^{\int _{}^{\ln \left (x \right )}\operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} a}{\textit {\_a}^{3} a -\textit {\_a}^{2} a +b}d \textit {\_a} \right )-\textit {\_b} +c_{1} \right )d \textit {\_b} +c_{2}}\]