Помогите решить уравнение y''-10y'=x^2

Question

Помогите решить уравнение
y''-10y'=x^2

Answer 1

1. y'' - 10y' = 0
k^2 - 10k = 0
k = 0, 10
y0 = C1 + C2*e^10x

2. y = ax^3 + bx^2 + cx
y'' - 10y' = 6ax + 2b - 30ax^2 - 20bx - 10c = x^2
-30a = 1 --> a = -1/30
6a - 20b = 0 -> b = -1/100
2b - 10c = 0 -> c = -1/500
y1 = -x^3/30 - x^2/100 - x/500

==>

y = C1 + C2*e^10x - x^3/30 - x^2/100 - x/500