Determine the explicit general solution to for solutions satisfying

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Determine the explicit general solution to

\dfrac{dy}{dx}=e^{x}(y-4)^{2}

for solutions satisfying

y(x)\neq 4

. Write

y

in terms of

x

and an arbitrary constant, and specify the branch condition that keeps

y

distinct from

4