ODE
\[ y'(x)=y(x) f'(x)+f(x) f'(x) \] ODE Classification
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Book solution method
Linear ODE
Mathematica ✓
cpu = 0.163052 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -f(x)+c_1 e^{f(x)}-1\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 15
\[[y \left (x \right ) = -f \left (x \right )-1+{\mathrm e}^{f \left (x \right )} \textit {\_C1}]\] 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))
Maple raw output
[y(x) = -f(x)-1+exp(f(x))*_C1]