Rewrite a Differential Equation

[619313]

1. I am studying for finals and I am trying to figure out how the author solved this

dy/dx = 4*e^(0.8*x)-0.5y and y(0) =2

Rewrite into the form

y = 4/1.3 *(e^(0.8x) - e^(-0.5x)) + 2e^(-0.5x)

I solved by P(x) = 0.5y and Q(x) = 4*e^(0.8x)

I have tried this numerous times and the closest I come is:

y = 4/1.3 *(e^(0.8x))

Any help would be much appreciated.

 

[ideasrule]

You probably forgot the final constant. On this webpage, it's the "c" in equation 14: http://mathworld.wolfram.com/First-OrderOrdinaryDifferentialEquation.html