- #1
SYoungblood
- 64
- 1
Homework Statement
Find the general solution to the equation.
Homework Equations
(dy/dx) - y - e^3x=0
The Attempt at a Solution
[/B]
I rewrote this as dy/dx - y = e^3x
This is a linear first order ODE, in the form dy/dx + P(x)y = f(x)
P(x) = 1; f(x) = e^3x
The integrating factor = e^(integral)P(x) dx = e^(integral) 1* dx = e^x
Set the LHS equal to the integrating factor, e^x * y, and multiply the RHS by the integrating factor e^x)
d/dx (ye^x) = e^x e^3x
(integral) d/dx (ye^x) =(integral) e^(3x^2) dx
On the LHS, the integral and d/dx cancel out, but I am getting a ridiculously complicated integral that I just know isn't right on the RHS, and I am not sure where I went astray.
Thank you for your time,
SY