2.1678   ODE No. 1678

1. Problem in Latex
2. Mathematica input
3. Maple input

$$x^2{y}^{″}(x)-\sqrt{a{x}^2{y}^{\prime }(x{)}^2+by(x{)}^2}=0$$ ✗ Mathematica : cpu = 1.62151 (sec), leaf count = 0 , 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 = 0.277 (sec), leaf count = 60

$$\{y\left(x\right)-{\mathrm{e}}^{{\int }^{\ln \left(x\right)}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}-y\left(x\right){({\mathit{\_}\mathit{a}}^{2}y\left(x\right)-y\left(x\right)\mathit{\_}\mathit{a}-\sqrt{{\left(y\left(x\right)\right)}^2({\mathit{\_}\mathit{a}}^{2}a+b)})}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1})d\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{2}}=0\}$$