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 = 1.3289 (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
\[ \left \{ y \left ( x \right ) -{{\rm e}^{\int ^{\ln \left ( x \right ) }\!{\it RootOf} \left ( \int ^{{\it \_Z}}\!-{y \left ( x \right ) \left ( {{\it \_a}}^{2}y \left ( x \right ) -{\it \_a}\,y \left ( x \right ) -\sqrt { \left ( y \left ( x \right ) \right ) ^{2} \left ( {{\it \_a}}^{2}a+b \right ) } \right ) ^{-1}}{d{\it \_a}}-{\it \_b}+{\it \_C1} \right ) {d{\it \_b}}+{\it \_C2}}}=0 \right \} \] 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),'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