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 = 0.0791582 (sec), leaf count = 13
\[\left \{\left \{y(x)\to c_2 \sec \left (c_1+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 17
\[ \left \{ -{\it \_C1}\,\sin \left ( x \right ) +{\it \_C2}\,\cos \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{-1}=0 \right \} \] 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),'implicit')
Maple raw output
-_C1*sin(x)+_C2*cos(x)+1/y(x) = 0