# Homework Help: Differential Equations [Show every member is a solution]

1. Sep 8, 2009

### Jay J

problem resolved

Last edited: Sep 8, 2009
2. Sep 8, 2009

### Staff: Mentor

You should have gotten two specific values for r1 and r2, one of which happens to be a fraction. Show that the function y = aer_1 x + ber_2 x is a solution to your differential equation. That's it.

3. Sep 8, 2009

### Jay J

I did get 2 answers, r= -1 and r=1/2. So now just plug those into the equation in part b ?

4. Sep 8, 2009

### Staff: Mentor

Yes. Then for that function, show that 2y'' + y' - y = 0.

5. Sep 8, 2009

### Jay J

O, okay thank you , it was really confusing me

6. Sep 8, 2009

### Jay J

When I Plugged back into 2y'' + y' -y = 0 I get 2ae-x+1/2be1/2x -ae-x +1/2be1/2x -ae-x -be1/2x=0

and theres nothing to cancel out :uhh:?

Help?

7. Sep 8, 2009

### Staff: Mentor

2ae-x+1/2be1/2x -ae-x +1/2be1/2x -ae-x -be1/2x = e-x(2a - a - a) + e.5x(.5b + .5b - b) = ?

8. Sep 8, 2009

### Jay J

ahh totally 4got about that ex . . lets see what I can do now lol

9. Sep 8, 2009

### Jay J

um I am still having some trouble with this . . cause even after factoring it your left with 2 unknown variables so how are you to prove it?

10. Sep 8, 2009