Finding Solutions to IVPs with Continuous Coefficients

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Homework Statement


Find all solutions of the IVP y'' + a(t)y' + b(t)y = 0, y(t0) = 0, y'(t0) = 0 where t0 is any fixed point on the t-axis and the coefficients are continuous.


The Attempt at a Solution


I know this has to do with the Existence and Uniqueness theorem. How would I apply that and solve this? Is the general solution y = c1y1 + c2y2? I'm not sure how to solve this...
 
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