Question

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

First order differential equations
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
$$y= e^{(e^{4x}/4+c)}+3$$