The special solution form of differential equation y '' - 2Y '+ y = (x ^ 2) * (e ^ x) is | Math enthusiast | Mathematical art

The special solution form of differential equation y '' - 2Y '+ y = (x ^ 2) * (e ^ x) is

The homogeneous form of the equation is as follows
y''-2y'+y=0
The characteristic equation is as follows
λ^2-2λ+1=0
λ = 1 (multiple roots)
Also: q = x ^ 2 * e ^ x
1 is the multiple root of the characteristic equation,
Therefore, let a special solution of the equation be:
Y * = x ^ 2 (AX ^ 2 + BX + C) * e ^ x is brought into the equation to solve a, B and C
The solution of the original equation is as follows
y=Ce^x+y*

RELATED INFORMATIONS

1. General solution of differential equation (x + 1) y '- 2Y = (x + 1) ^ 5
2. Find the general solution of the following differential equation y '- (2Y) / (x + 1) = (x + 1) ^ 3
3. Find the general solution of the differential equation y '' + 2Y '- 48y = e ^ X
4. General solution of differential equation y '' - 2Y '= x
5. General solution of differential equation y "+ 2Y = x
6. Finding the general solution of differential equation y '' + 2Y '= - x + 3
7. Special solution of differential equation y '+ y = 1 satisfying initial condition y (0) = 0
8. Find the solution of the differential equation y '' = y'e ^ y satisfying the condition y (0) = 0, y '(0) = 1
9. Special solution of differential equation y '= y satisfying initial condition y (0) = 1 Right away
10. Solving differential equation y * y '' - (y ') ^ 2-y ^ 2 * y' = 0
11. The special solution form of differential equation y '' - 2Y '+ 2Y = xsinx is y*= I figured it out to be (AX + b) (ccosx + dsinx), but the answer is (AX + b) cosx + (Cx + D) SiNx
12. The special solution of differential equation 2Y (1 + x) y '= 4 + y ^ 2, when x = 3, y = 2
13. A special solution of differential equation y '' + 2Y '+ y = x ^ 2 + 1 is obtained
14. A special solution of differential equation y "+ 2Y '+ y = 3 is y*=
15. Find the general solution of differential equation 1, y '= 2xe (- y) 2, y' = x + y 3, 3Y '' + 2Y '- y = 0.4, y' '- 2Y' + 2Y = 2e (- x) The ones in brackets are all at the top right of the letter. Because I don't know how to type it-
16. General solution of differential equation y '' - 3Y '+ 2Y = 3
17. Second order nonhomogeneous differential equation y '' + 2Y '+ y = (e ^ (- x)) / X Y '' + 2Y '+ y = (e ^ (- x)) / X
18. General solution of differential equation y '= (1-y) / X Please give me your advice
19. General solution of differential equation y '= y (1-x) / X
20. Find the general solution of the following differential equation y ″ + y ′ = x + 1 Big one, high number, do the right score,