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 = 0.0168895 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \log \left (c_1+x\right )+c_2-2 \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.26 (sec), leaf count = 16
\[ \left \{ x{{\rm e}^{y \left ( x \right ) }}+{\it \_C2}-{\frac {{\it \_C1}}{x}}=0 \right \} \] 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),'implicit')
Maple raw output
x*exp(y(x))+_C2-1/x*_C1 = 0