The Student Room Group

Quick differential equation problem - help please! (rep)

Hi, I was off school today so I missed learning about this in class today. I've been given the question:

"Find the particular solution to
d2y/dx2 - 10dy/dx + 25y = 0 given that when x=0, y=2 and dy/dx=2"

Now I've found the general solution and A, but I'm not sure how to use dy/dx=2 to find B in the particular solution. I know it's probably really simple but i can't find it in my notes and have been ill so have basically had to teach myself differential equations over the weekend! :smile: thanks in advance to anyone that can help.
friendlyneutron
Hi, I was off school today so I missed learning about this in class today. I've been given the question:

"Find the particular solution to
d2y/dx2 - 10dy/dx + 25y = 0 given that when x=0, y=2 and dy/dx=2"

Now I've found the general solution and A, but I'm not sure how to use dy/dx=2 to find B in the particular solution. I know it's probably really simple but i can't find it in my notes and have been ill so have basically had to teach myself differential equations over the weekend! :smile: thanks in advance to anyone that can help.



general;

y= (A+Bx)e5x

y=2= A

dy/dx = 5Ae5x + Be5x + 5Bxe-5x

dy/dx = 2 = 10 + B

=> B=-8
Ah excellent, thanks! seems so obvious now lol. :smile: rep comin your way!
Check your thread in the other maths forum, because I don't think KM is correct.

Ifyou use the solution y = ekx you'll find k=5, not -5. You can check by putting in y = e5x and seeing it works :smile:
He's on the ball this one, missed the minus o.O ...will edit accordingly
I wouldn't have noticed it off the top of my head normally, it's just the coefficents 1, -10 and 25 said to me (x-5)2 immediately. If there'd been two different roots, it would have been less apparent.