Solve the boundary value problem y 2y 2y 0 y0 1 ypi2 0S

Solve the boundary value problem y\" + 2y\' + 2y = 0, y(0) = 1, y\'(pi/2) = 0.

Solution

The given equation in symbolic form is( D² + 2D +2)Y =0

The auxialary equation is m²+2m+2=0

m1= -1+i,m2= -1-i

Therefore,

Roots are imaginary roots,so the solution is

y= e^-x[c1cosx+c2sinx]

Given that y(0)=1

then substitute value in y

1=e^-0[c1cos0+c2sin0]

1=1[c1+0]

c1=1