ODE
\[ y'(x)=y(x) f'(x)+f(x) f'(x) \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00774583 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_1 e^{f(x)}-f(x)-1\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) =-f \left ( x \right ) -1+{{\rm e}^{f \left ( x \right ) }}{\it \_C1} \right \} \] Mathematica raw input
DSolve[y'[x] == f[x]*f'[x] + y[x]*f'[x],y[x],x]
Mathematica raw output
{{y[x] -> -1 + E^f[x]*C[1] - f[x]}}
Maple raw input
dsolve(diff(y(x),x) = f(x)*diff(f(x),x)+diff(f(x),x)*y(x), y(x),'implicit')
Maple raw output
y(x) = -f(x)-1+exp(f(x))*_C1