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Question Number 1056 by 123456 last updated on 25/May/15
y″+y=8cos(t)y(0)=+1y′(0)=−1
Commented by prakash jain last updated on 26/May/15
charactersticequationr2+1=0yh=c1cost+c2sint
Answered by prakash jain last updated on 26/May/15
yp=ktsintyp′=ktcost+ksintyp″=−ktsint+kcost+kcostyp″+y=2kcost=8cost⇒k=4y=yp+yh=c1cost+c2sint+4tcosty(0)=1⇒c1=1y′=4tcost+4sint−c1sint+c2costy′(0)=−1⇒c2=−1y=cost−sint+4tsint
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