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 = 0.344757 (sec), leaf count = 9
\[\{\{y(x)\to c_2 x\}\}\]
Maple ✓
cpu = 0.044 (sec), leaf count = 26
\[\left [y \left (x \right ) = \frac {\textit {\_C1}^{2} x}{4 \textit {\_C2}}+\textit {\_C1} x \ln \left (x \right )+\textit {\_C2} x \ln \left (x \right )^{2}\right ]\] 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))
Maple raw output
[y(x) = 1/4*_C1^2/_C2*x+_C1*x*ln(x)+_C2*x*ln(x)^2]