Differential Equation problem?

Question

solve the given diff. equation:

dy/dx + y = 4e^x

Answer 1

dy/dx + y = 4e^x

P(x) =1 and Q(x) =4e^x

Use an Integrating Factor (IF).

IF =e^∫Pdx

IF = e^(∫1dx) = e^x

(IF)y =∫(IF)(Q(x))dx

(e^x)y =∫(e^x)(4e^x)dx

(e^x)y =4∫(e^2x)dx

(e^x)y =2(e^2x)+C

y=2e^x+C'