ODE
\[ x^2 y''(x)=\sqrt {a x^2 y'(x)^2+b y(x)^2} \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 1.08256 (sec), leaf count = 0 , could not solve
DSolve[x^2*Derivative[2][y][x] == Sqrt[b*y[x]^2 + a*x^2*Derivative[1][y][x]^2], y[x], x]
Maple ✓
cpu = 1.382 (sec), leaf count = 60
\[\left [y \left (x \right )-{\mathrm e}^{\int _{}^{\ln \left (x \right )}\RootOf \left (\int _{}^{\textit {\_Z}}-\frac {y \left (x \right )}{\textit {\_a}^{2} y \left (x \right )-\textit {\_a} y \left (x \right )-\sqrt {y \left (x \right )^{2} \left (a \,\textit {\_a}^{2}+b \right )}}d \textit {\_a} -\textit {\_b} +\textit {\_C1} \right )d \textit {\_b} +\textit {\_C2}} = 0\right ]\] Mathematica raw input
DSolve[x^2*y''[x] == Sqrt[b*y[x]^2 + a*x^2*y'[x]^2],y[x],x]
Mathematica raw output
DSolve[x^2*Derivative[2][y][x] == Sqrt[b*y[x]^2 + a*x^2*Derivative[1][y][x]^2], y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = (a*x^2*diff(y(x),x)^2+b*y(x)^2)^(1/2), y(x))
Maple raw output
[y(x)-exp(Intat(RootOf(Intat(-y(x)/(_a^2*y(x)-_a*y(x)-(y(x)^2*(_a^2*a+b))^(1/2)),_a = _Z)-_b+_C1),_b = ln(x))+_C2) = 0]