6y''+y'-y=x^2-x+4e^(-3t)
"find a particular solution"
I get
-4*e^(-3t)-t^2-t-13
or
39/50*e^(-3t)-t^2-t-13
but apparently they both are wrong?
Can someone here help me confirm if they are right or wrong?
EDIT: I'm an idiot.
6y''+y'-y=x^2-x+4e^(-3t)
"find a particular solution"
I get
-4*e^(-3t)-t^2-t-13
or
39/50*e^(-3t)-t^2-t-13
but apparently they both are wrong?
Can someone here help me confirm if they are right or wrong?
EDIT: I'm an idiot.
Several comments:
0. You are mixing independent variables there. Are they all x's? Or all t's?
1. Checking to see if your guess works is usually fairly straight-forward. Just plug your solution into the DE and see if it satisfies it.
2. Assuming your RHS is all x's, I would try a particular solution of the form y_p = A x^2 + B x + C + D exp(-3x).
3. Finally, you spell it "differential", not "differencial".