# Solve differential equation dy/dx = e^4x(y-3)

Question
Solve differential equation $$dy/dx = e^4x(y-3)$$

2020-10-26
$$dy/dx= e^(4x)(y-3)$$
$$dy/dx= (e^(4x))(y-3)$$
$$dy/((y-3))= (e^(4x))dx$$
$$int 1/(y-3) dy= int (e^(4x))dx$$
$$ln(y-3)= e^(4x)/4+c$$
Apply exponential on both sides
$$e^(ln(y-3))= e^((e^(4x)/4+c))$$
Thus, the solution of the given first order differential equation is
$$y= e^((e^(4x)/4+c))+3$$

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