# Thread: Urgent: ......differential equation (another).

1. ## Urgent: ......differential equation (another).

Hi it's me again.

I have another couple of problems I need to solve. (Same as before I have no idea what I am doing, so as much detail as you are willing to give, will be greatly appreciated).

(Problem 1) Find the general solution of:

d^2/dx^2 - 4 dy/dx + 5y = 0

(Problem 2) Find the particular solution of:

d^2y/dx^2 - y = e^2x , y(0)=0, y'(0)=1,

Any assistance will be greatly appreciated!!!

Thank you math_Newbie.

2. Let's use Laplace.

$\displaystyle y''-y=e^{2x}, \;\ y(0)=0, \;\ y'(0)=1$

$\displaystyle p^{2}Y-py(0)-y'(0)-Y=\frac{1}{p-2}$

Sub in the IC's:

$\displaystyle p^{2}Y-1-Y=\frac{1}{p-2}$

and solve for Y and you get:

$\displaystyle Y=\frac{1}{(p-2)(p+1)}$

Now, find the inverse Laplace of this and we see that we get:

$\displaystyle y=\frac{e^{2t}-e^{-t}}{3}$

3. Thank you for the pointers, though I am still a little unsure

Does anyone have any ideas about the first problem?

(Problem 1) Find the general solution of:

d^2/dx^2 - 4 dy/dx + 5y = 0

Thank you math_Newbie.

4. Originally Posted by math_Newbie
Thank you for the pointers, though I am still a little unsure

Does anyone have any ideas about the first problem?

(Problem 1) Find the general solution of:

d^2/dx^2 - 4 dy/dx + 5y = 0