you would do this using the product rule.
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.?
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.