Question

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

First order differential equations
ANSWERED
asked 2020-10-25
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
\(y= e^{(e^{4x}/4+c)}+3\)

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