So I differentiated the second equation with respect to t:Aha , try differentiating one of the equations and tell me if you got any ideas .
That seems a not-easy problem to deal with if we try the other differentiation we getSo I differentiated the second equation with respect to t:
v'' = -du/dt
Then I substitute first equation for du/dt:
v'' = -(v - w(t-5)) = -v + w(t-5)
v'' + v - w(t-5) = 0
Does it become: v'' + v = wt - 5w ? How does keeping the w matter?
And then I solve the IVP. Is this correct? But what if w is a function of t? Then I am confused, is that possible? Thank you for answering.
Can w(t-5) be the Heavyside unit function?That seems a not-easy problem to deal with if we try the other differentiation we get
\(\displaystyle u''+ut = 2- w \)
The problem will get more complicated if assumed that $w$ a function because we have a three functions and two equations !
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It might be solvable by Laplace but I don't know whether it is an acceptable solution ?