Thread: Another Undetermined Coefficient question

y" + y' = 3x^2

Here's the work I've done:

yc:

1. r^2 + r = 0
2. r(r + 1) = 0
3. r=0, -1
4. Thus, yc= c1 +c2e^-x

How do I solve for yp? Thanks,

JN

Originally Posted by Jim Newt

y" + y' = 3x^2

Here's the work I've done:

yc:

1. r^2 + r = 0
2. r(r + 1) = 0
3. r=0, -1
4. Thus, yc= c1 +c2e^-x

How do I solve for yp? Thanks,

JN

To solve for , we assume it takes on the form of a second degree polynomial :

Now plug into the DE and solve for the unknown coefficients:




Therefore, we have:



Comparing the coefficients, we have:



This implies that both A and B equal .

Therefore, .