ODE
\[ x^2 y''(x)+x^2 y'(x)^2+4 x y'(x)+2=0 \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.285526 (sec), leaf count = 17
\[\{\{y(x)\to -2 \log (x)+\log (x+c_1)+c_2\}\}\]
Maple ✓
cpu = 0.442 (sec), leaf count = 15
\[\left [y \left (x \right ) = \ln \left (\frac {-\textit {\_C2} x +\textit {\_C1}}{x^{2}}\right )\right ]\] Mathematica raw input
DSolve[2 + 4*x*y'[x] + x^2*y'[x]^2 + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2] - 2*Log[x] + Log[x + C[1]]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x^2*diff(y(x),x)^2+4*x*diff(y(x),x)+2 = 0, y(x))
Maple raw output
[y(x) = ln((-_C2*x+_C1)/x^2)]