ODE
\[ 2 x^2 y(x) y''(x)=x^2 y'(x)^2-y(x)^2 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0578231 (sec), leaf count = 9
\[\left \{\left \{y(x)\to c_2 x\right \}\right \}\]
Maple ✓
cpu = 0.083 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( 2\,{\it \_C2}\,\ln \left ( x \right ) +{\it \_C1} \right ) ^{2}}{4\,{\it \_C2}}} \right \} \] Mathematica raw input
DSolve[2*x^2*y[x]*y''[x] == -y[x]^2 + x^2*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> x*C[2]}}
Maple raw input
dsolve(2*x^2*y(x)*diff(diff(y(x),x),x) = x^2*diff(y(x),x)^2-y(x)^2, y(x),'implicit')
Maple raw output
y(x) = 1/4*x*(2*_C2*ln(x)+_C1)^2/_C2