Differentiation help to find particular solution to initial value problem

• Feb 16th 2008, 12:29 PM
moolimanj
Differentiation help to find particular solution to initial value problem
Hi All

I need to find a particular solution to initial value problem but I'm stuck.

The problem is (attachment 666)

I have found the general solution to be the following (attachment 777) but now I'm stuck. Do I need to differentiate this and if so, how would I do this for the terms with e^x.?
• Feb 16th 2008, 12:50 PM
Peritus
you would do this using the product rule.
• Feb 16th 2008, 12:57 PM
moolimanj
does that mean that if i differentiate I will get the particular solution to the initial value problem?
• Feb 16th 2008, 03:58 PM
mr fantastic
Quote:

Originally Posted by moolimanj
does that mean that if i differentiate I will get the particular solution to the initial value problem?

No.

You differentiate to get y'(x). You want y'(x) in order to use the boundary condition y'(0) = 3. You substitute x = 0 into the derivative and put the result equal to 3. That gives you a linear equation in C and D.

You then use the boundary condition y(0) = -2. You substitute x = 0 into y and put the result equal to -2. That gives you a linear equation in C and D.

Now solve the two linear equations simultameously to get the value of C and D.