4.1.38 \(y'(x)=y(x) f'(x)+f(x) f'(x)\)

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

\[ \left \{ y \relax (x ) =-f \relax (x ) -1+{{\rm e}^{f \relax (x ) }}{\it \_C1} \right \} \] 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