\[ x^2 y''(x)-\sqrt {a x^2 y'(x)^2+b y(x)^2}=0 \] ✗ Mathematica : cpu = 0.800732 (sec), leaf count = 0
DSolve[-Sqrt[b*y[x]^2 + a*x^2*Derivative[1][y][x]^2] + x^2*Derivative[2][y][x] == 0,y[x],x]
, could not solve
DSolve[-Sqrt[b*y[x]^2 + a*x^2*Derivative[1][y][x]^2] + x^2*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.86 (sec), leaf count = 60
dsolve(x^2*diff(diff(y(x),x),x)-(a*x^2*diff(y(x),x)^2+b*y(x)^2)^(1/2)=0,y(x))
\[y \left (x \right )-{\mathrm e}^{\int _{}^{\ln \left (x \right )}\RootOf \left (\int _{}^{\textit {\_Z}}-\frac {y \left (x \right )}{\textit {\_a}^{2} y \left (x \right )-\textit {\_a} y \left (x \right )-\sqrt {y \left (x \right )^{2} \left (\textit {\_a}^{2} a +b \right )}}d \textit {\_a} -\textit {\_b} +c_{1}\right )d \textit {\_b} +c_{2}} = 0\]