\(dy/dx= e^(4x)(y-3)\)

\(dy/dx= (e^(4x))(y-3)\)

\(dy/((y-3))= (e^(4x))dx\)

\(int 1/(y-3) dy= int (e^(4x))dx\)

\(ln(y-3)= e^(4x)/4+c\)

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

\(y= e^((e^(4x)/4+c))+3\)

\(dy/dx= (e^(4x))(y-3)\)

\(dy/((y-3))= (e^(4x))dx\)

\(int 1/(y-3) dy= int (e^(4x))dx\)

\(ln(y-3)= e^(4x)/4+c\)

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

\(y= e^((e^(4x)/4+c))+3\)