Differential equation/characteristic equation

[Resa]

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)

 

[LCKurtz]

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

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?

 

[Resa]

ummm is it
y(t)=Ce^pt+C₂e^p2t
I really don't know...

 

[Resa]

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?

I figured out the answers

 

[Mark44]

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)

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

 

[Resa]

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

yes