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 = 0.30506 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {c_2 e^x}{\sqrt {1-2 e^{x+c_1}}}\right \}\right \}\]
Maple ✓
cpu = 0.695 (sec), leaf count = 67
\[\left [y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (\textit {\_C1} \,{\mathrm e}^{x}-\textit {\_C2} \right ) {\mathrm e}^{2 x}}}{2 \left (\textit {\_C1} \,{\mathrm e}^{x}-\textit {\_C2} \right )}, y \left (x \right ) = \frac {\sqrt {2}\, \sqrt {\left (\textit {\_C1} \,{\mathrm e}^{x}-\textit {\_C2} \right ) {\mathrm e}^{2 x}}}{2 \textit {\_C1} \,{\mathrm e}^{x}-2 \textit {\_C2}}\right ]\] 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))
Maple raw output
[y(x) = -1/2*2^(1/2)*((_C1*exp(x)-_C2)*exp(2*x))^(1/2)/(_C1*exp(x)-_C2), y(x) = 1/2*2^(1/2)*((_C1*exp(x)-_C2)*exp(2*x))^(1/2)/(_C1*exp(x)-_C2)]