4.1873   x2y′′(x) = ∘ax2y-′(x)2-+-by(x)2

ODE

x2y′′(x) = ∘ax2y-′(x-)2-+by(x)2

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 1.3289 (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 = 0.289 (sec), leaf count = 60

                  (       (                         )          )
{       ∫ln(x)RootOf ∫-Z−y(x)-a2y(x)− ay(x)−∘ (y(x))2(-a2a+b) −1d-a−-b+ C1 d-b+ C2    }
 y (x) − e                                                              = 0

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),'implicit')

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