Sciences (calc lus of ariations and linear integral equation find the approximate the smallest eigen value à of v +ay =y-y let solution be y = = c(x- x) ex. 0,

Sciences (Calc lus of ariations and Linear Integral Equation Find the approximate the smallest eigen value à of v +Ay =y-y Let solution be y = = c(x- x) Ex. 0, y(0) = y(1) = 0 and FX, Y. Y) Sol. I= c(1-2x-c(x-xF]dx =0 dc 2o(1-2x) -2c(x- x]dx = 0 C1-2x) dx-a,x-xdx 1-4x+4x )dx = , (x-2x+x Jdx x-2x 123-3 10-15 6 30 3-6+4 -x- = 10 3 which is the least approximate eigen value of the given differential equation, From the Strum-Liouville problem it is known that eigen values are given by (((in this problem F contain no x so how y=c(x-x^2) is happened