How to find two constants in an equation

[Aerosion]

Homework Statement

i'm trying to find two constants in the same equation. its an initial value problem

there's a two parameter family x=c1cost+c2sint with initial conditions x''+x=0, x(pi/6)=1/2, and x'(pi/6)=0

so I'm trying to find c1, and i equate the problem to 1/2 and subsitute the t's for pi/6, so it looks like

1/2=c1cos(pi/6)+c2sin(pi/6)

which of course equals sqrt(3)c1/2 + c2/2

but how do i get the values of c1 and c2? I've tried everything and i need them to find a solution

Homework Equations

The Attempt at a Solution

 

[sutupidmath]

well, you already found one relation sqrt(3)c1/2 + c2/2=1/2, to find another relation,

take the first derivative of x=c1cost+c2sint, and apply the second contidion that you are given x'(pi/6)=0

so you'll get two lin. eq in two unknowns, c1,c2, and u should be able to solve it.