ODE
\[ y(x) y''(x)=2 y'(x)^2+y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.330601 (sec), leaf count = 13
\[\{\{y(x)\to c_2 \sec (x+c_1)\}\}\]
Maple ✓
cpu = 0.398 (sec), leaf count = 16
\[\left [y \left (x \right ) = \frac {1}{\sin \left (x \right ) \textit {\_C1} -\textit {\_C2} \cos \left (x \right )}\right ]\] Mathematica raw input
DSolve[y[x]*y''[x] == y[x]^2 + 2*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*Sec[x + C[1]]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = 2*diff(y(x),x)^2+y(x)^2, y(x))
Maple raw output
[y(x) = 1/(sin(x)*_C1-_C2*cos(x))]