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When I have the differential equation

[tex]\frac{dY(x)}{dx} = -k^2 Y(x)[/tex]

The solution is of course harmonic oscillation, however, looking at various places I see the solution given as:

[tex]Y(x) = A cos(kx) + B sin(kx)[/tex]

instead of

[tex]Y(x) = A cos(kx + \phi_1) + B sin(kx + \phi_2)[/tex]

Isnt Equation 2 a more general solution than Equation 1? Or is there some reasoning (probably is) to make the phase angles go away?

Thank you.