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

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

Answers (1)

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
\(y= e^((e^(4x)/4+c))+3\)
0

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