2.1678   ODE No. 1678

\[ x^2 y''(x)-\sqrt {a x^2 y'(x)^2+b y(x)^2}=0 \]

✗ Mathematica : cpu = 1.16828 (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 = 0.306 (sec), leaf count = 57

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))
 

\[y \left (x \right )-{\mathrm e}^{\int _{}^{\ln \left (x \right )}\operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {y \left (x \right )}{-\textit {\_a}^{2} y \left (x \right )+\textit {\_a} y \left (x \right )+\sqrt {y \left (x \right )^{2} \left (\textit {\_a}^{2} a +b \right )}}d \textit {\_a} -\textit {\_b} +c_{1} \right )d \textit {\_b} +c_{2}} = 0\]