I want to pass from a solution of the form $u(\phi)=c_1 \sin (\phi) + c_2 \cos (\phi)$ to a one that look like this $u(\phi)=A \epsilon \cos (\phi-\phi_0)$
How i can get it analytically? And what is the value of the constant $A$, is it totally arbitrary? Thanks.
EDIT: Ok, i know that the boundary values determine a unique solution. But i.e binet's formula has the form $u'' +u = -k$ and the given answer answer (in the paper) is $u = -k + k \epsilon \cos (\phi - \phi _0 )$ where $\epsilon$ and $\phi _0 $ are the boundary values. so $A$ is equaled to $k$ arbitrarily.