Thread: Constant coefficients initial value problem

y" -4y' + 3y = 0 y(0)= -1 ; y'(0)= 3

Here's how I tried to solve it:
1. r^2 - 4r + 3 = 0
2. (r-1)(r-3) = 0
3. r= 1, 3
4. Thus y=c1(e^x) + c2(e^3x)

But now I'm stuck. How do I use the initial values to solve for c1, c2?

Thanks,

Jim

Originally Posted by Jim Newt

y" -4y' + 3y = 0 y(0)= -1 ; y'(0)= 3

Here's how I tried to solve it:
1. r^2 - 4r + 3 = 0
2. (r-1)(r-3) = 0
3. r= 1, 3
4. Thus y=c1(e^x) + c2(e^3x)

But now I'm stuck. How do I use the initial values to solve for c1, c2?

Thanks,

Jim

You now have a system of equations like so:




I'm sure you can finish this!