General solution of differential equation y '' - 2Y '= x

General solution of differential equation y '' - 2Y '= x

The characteristic equation is: λ ^ 2-2, λ = 0, then: λ = 0,2
So Y1 = C1E ^ (2x) + C2
Let y * = ax ^ 2 + BX
y*'=2ax+b
y*"=2a
Substituting: 2a-2 (2aX + b) = x, the comparison coefficient is: - 4A = 1, 2a-2b = 0, a = b = - 1 / 4, so y * = - (x ^ 2 + x) / 4
So the general solution is y = Y1 + y * = C1E ^ (2x) + C2 - (x ^ 2 + x) / 4

Elden Ring Premiere

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