Proving Uniqueness of Complementary Solution for y(x)=y_c+y_p

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Homework Statement



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The Attempt at a Solution



I can show that the complementary solution y_c solves L[y]=0 and any initial conditions for a unique choice of the c_i's, using the standard "Wronskian and invertible matrix proof". I'm stuck on this part though, how can I prove it for y(x) = y_c + y_p?
 

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Bump. please help :)
 
Could anyone offer a tip please? This is due tomorrow.
 

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