Question

using the elimination of arbitrary constant, how can i solve for these
1. y = c1e^x=c2xe^x
2. y = Ae^2x + Bxe^x
3. y = (c1e^2x)(cos3x) + (c2e^2x)(sin3x)
4. y = c1x^2 + c2e^2x

Answer 1

Seeing as this is a differential equations question, by any chance, are there any initial values?

Answer 2

power series?

Answer 3

as @SithsAndGiggles said, I think you should have initial values to eliminate a constant.
One more question: y =... is the combination of y_H +y_P ?