Solve y′′(t)+2y′(t)+2y(t)=H(t); y(0)=1 ;y′(0)=0 where H(t)=2t+3 , 0≤t<1 H(t)=3t+1, t≥1

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A: To solve this problem first we write the system as a system of linear homogeneous differential…

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A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy…

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

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Q: (b) Solve 1 y +-y= 0, t> 0. t

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Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

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A: Given differential equation is                  dydx(1+2y)-2x=0      ⟹   (1+2y)dy=2xdx Intergrating…

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Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

A: Given:-           The differential equation  is:…