Question

15 panti Pre Annwers 20E0Mote 4442 My No Selve the ghven intiel-vaue prablem in which the irput fnction g)in dsconti s So the problem on twenervalsnd then d soluton so thaty nd con aa-) 2 10-x C0)-0, yT0)-0where 0, - . Need Help? Wh Te r

Answer 1

y^'' - 2y^' + 10 y = g (x): y (0) = 0 y^' (0) = 0 g (x) ={ 70 0 lessthanorequalto x lessthanorequalto pi 0 x > pi for 0 lessthanorequalto x lessthanorequalto pi y^'' - 2y^' + 10y = 70 general solution to 1 is y (x) = y_h (x) + y_p (x) where y_h (x) is solution of corresponding homogenous equation y^n - 2y^' + 10y = 0 y_p (x) = 1/D^2 - 2D + 10 (70) consider , y^'' - 2y^' + 10y = 0 Auxiliary equation is lambda^2 - 2 lambda + 10 = 0 Therefore lambda = -(-2) plusminus squareroot (-2)^2- 4 times 1 times 10/2 times 1 2 plusminus squareroot -36/2 = 2 plusminus 6i/2 = 1 plusminus 3i Rule: i. > if if auxillary eq^n