ODE
\[ y(x) y''(x)=-3 y(x) y'(x)+3 y'(x)^2+y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0646049 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {c_2 e^x}{\sqrt {1-2 e^{c_1+x}}}\right \}\right \}\]
Maple ✓
cpu = 0.039 (sec), leaf count = 20
\[ \left \{ -{{\rm e}^{-x}}{\it \_C1}+{\it \_C2}-{\frac {{{\rm e}^{x}}}{2\, \left ( y \left ( x \right ) \right ) ^{2}}}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == y[x]^2 - 3*y[x]*y'[x] + 3*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (E^x*C[2])/Sqrt[1 - 2*E^(x + C[1])]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+y(x)^2, y(x),'implicit')
Maple raw output
-exp(-x)*_C1+_C2-1/2/y(x)^2*exp(x) = 0