# Differential equation/characteristic equation

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1. Nov 18, 2014

### Resa

• Member warned about not using the homework template
Any help is appreciated

1.)----Find the Character equation for the diff equation d^2y/dx^2-4dy/dx+3y=0 with initial conditions y(0)=0 and y'(0)=12 find the solution y(t)

(this is what I have gotten so far on this part) p^2+4p+3=0
then (p-1)(p-3)=0 so p1=1 and p2=3??????
not really sure what to do after that

2.)----then solve the diff equation 4dy/dx+16y=80 where y(0)=6 (hint is that you have the homogenous solution in the problem above)

2. Nov 18, 2014

### LCKurtz

You mean $p^2 \color{red}{-} 4p +3$. You got the characteristic equation by assuming solutions of the form $e^{pt}$. So what do you get for your general solution?

3. Nov 18, 2014

### Resa

ummm is it
y(t)=Cept+C2ep2t
I really dont know...

4. Nov 18, 2014

### Resa

5. Nov 18, 2014

### Staff: Mentor

Despite the hint, I don't see that this is related to question 1 at all. Have you been able to solve this problem?

6. Nov 18, 2014

yes