Resolva a equação diferencial de segunda ordem abaixo e encontre a solução particular dos (PVI)
y" + 2y' + y = ( 2 + t )
y(0) = 0
y'(0) = 1
y" + 2y' + y = ( 2 + t )
y(0) = 0
y'(0) = 1
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y" + 2y' + y = (2 + t)*e^-t
y(0) = 0
y'(0) = 1
y(t) = c2*e^(-t)*t + c1*e^(-t) + e^(-t) t^3/6 + e^(-t)*t^2
y(0) = c1 = 0
y'(t) = -1/6 e^(-t) (6 c1 + 6 c2 (t - 1) + t (t (t + 3) - 12))
y'(0) = -1/6*(6c2*(-1) = 1
c2 = 1
y(t) = e^(-t)*t + (1/6)*e^(-t)*t^3 + e^(-t)*t^2
y'(t) = -1/6 e^(-t) (6(t - 1) + t (t (t + 3) - 12))
y"(t) = e^(-t) (t^3/6 - 2t)