Find the solution to the initial value problem

[mad_monkey_j]

Homework Statement

Find the solution to the initial value problem
dy/dx - y = e^3x
y(0) = 3

Homework Equations

e^∫p(x)

The Attempt at a Solution

Do I treat p(x) = -1?
I(x) = e^∫-1 = e^-x
e^-x(dy/dx) - ye^-x = e^3x . e^-x
e^-x(dy/dx) - e^-x . y = e^2x
e^-x . y = ∫e^2x
y = (2e^2x + c)/(e^-x)
y = C+2e^3x?

 

[Hootenanny]

Homework Statement

Find the solution to the initial value problem
dy/dx - y = e^3x
y(0) = 3

Homework Equations

e^∫p(x)

The Attempt at a Solution

Do I treat p(x) = -1?
I(x) = e^∫-1 = e^-x
e^-x(dy/dx) - ye^-x = e^3x . e^-x
e^-x(dy/dx) - e^-x . y = e^2x
e^-x . y = ∫e^2x
y = (2e^2x + c)/(e^-x)
y = C+2e^3x?

Yes, in this case p(x)=-1. However, you're answer isn't correct as it doesn't satisfy the initial value problem. You have made a little slit in the second to last line of your working.