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4) solve the differential equation y"+y= èx Satisfying the initial condition Y(0)=1 , Y'(o)=-1

Answer 1

PAGE NO: soution. We have, y + y = e i - y lo=1 40) = -1 The auxillary equation associated with is equation homogenous m²+1=0 m² = -1 x m = i i . Y.(x) = q sinxe the cosa The particual solution will be of the - Uplt) = deux a up' = - A ex up" = Aet form, Substituting in the differential equation, we get - Rent A et = (-x * 2A=1 . Yp(x) = ax 0 4(x) = yc typ = asinx +C cosa t ex 416) = 1 + 1 = (a + 1 x C2 = 2 420) = -1 - - 1 - 4 - 1 x 9 = -2 The solution is given by a Jy) = 1 and I cose ter

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