Differential Equations Problem

1. Sep 13, 2006

Dao Tuat

Consider the differential equation d^2y/dx^2 + dy/dx - 6y = 0 with the initial conditions y(0)= 6 and y'(0)=2. Determine whether the following functions are solutions:

a. y=4e^(2x) + 2e^(-3x)

b. y=2e^(2x) + 4e^(-3x)

If someone could please at least help me get started on this I would appreciate it very much

Thanks,
Dao Tuat

2. Sep 13, 2006

Tomsk

You need to substitute the two solutions given into the differential equation, and see if they come to zero. I don't think they're asking you to solve it directly.

3. Sep 13, 2006

Be sure to also check that the solutions satisfy the given initial conditions.

4. Sep 14, 2006

Dao Tuat

So then neither a or b are solutions, right?

5. Sep 14, 2006

wurth_skidder_23

Only a. is a solution because b. doesn't satisfy y'(0) = 2 (y'(0) = -8). They both fit the equation, though, as can seen below.

(16e^(2x) + 18e^(-3x)) + (8e^(2x) - 6e^(2x)) - 6*(4e^(2x) + 2e^(-3x)
(8e^(2x) + 36e^(-3x)) + (4e^(2x) - 12e^(-3x)) - 6*(2e^(2x) + 4e^(-3x))

Last edited: Sep 14, 2006