# Thread: Differentiation help to find particular solution to initial value problem

1. ## 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.?

2. you would do this using the product rule.

3. does that mean that if i differentiate I will get the particular solution to the initial value problem?

4. 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.