Solve the Initial-value problem

[moy1989]

Hey guys, I need help with this one. I can't figure out what c1 and c2 are equal to.

y'' + y' - 2y = 0
y(0) = 1, y'(0) = 0

This is what I did:

r^2 + r - 2 = 0
(r+2)*(r-1) = 0
r = -2 and 1

So, y(t) = c1exp(-2t) + c2exp(t)

y(0) = 1 = c1 + c2

y'(0) = 0 = 2c1 + c2

So, now how do I find what c1 and c2 are equal to?

Thanks for any help.

 

[Deleted member 4993]

Hey guys, I need help with this one. I can't figure out what c1 and c2 are equal to.

y'' + y' - 2y = 0
y(0) = 1, y'(0) = 0

This is what I did:

r^2 + r - 2 = 0
(r+2)*(r-1) = 0
r = -2 and 1

So, y(t) = c1exp(-2t) + c2exp(t)

y(0) = 1 = c1 + c2 ..................................................................(1)

y'(0) = 0 = 2c1 + c2..................................................................(2)

So, now how do I find what c1 and c2 are equal to?

Thanks for any help.

You have two equations - (1) & (2) - and two unknowns (c[sub:2zkbh0zg]1[/sub:2zkbh0zg] & c[sub:2zkbh0zg]2[/sub:2zkbh0zg]) - system of linear equations - should have (must have) learnt to solve these in algebra.

In case you need a refresher - go to:

http://www.purplemath.com/modules/systlin4.htm