Question

Solve the IVP: y''+y=0, y(pi/3)=0, y'(pi/3)=2. Find y(pi/6)

Answer 1

So first, what's the general solution to

y'' + y = 0 ?

Answer 2

Do you know the general solution?

Answer 3

If not, just say so

Answer 4

I'm guessing not. The general solution is

y(x) = C1.sin(x) + C2.cos(x)

Now apply the initial conditions to solve for C1 and C2.

Answer 5

i got the first part. dont know how to solve the rest

Answer 6

So if y(pi/3) = 0, then
y(pi/3) = C1.sin(pi/3) + C2.cos(pi/3)
= C1.(sqrt(3)/2) + C2.(1/2) = 0

Find now the expression for y'(pi/3) = 2

and you'll have two simultaneous equations in C1 and C2 which you solve.