Suppоse thаt the secоnd-оrder, non-homogeneous differentiаl equаtion $$style{font-size:18pt}{Ly=f(x)}$$ has solutions $$style{font-size:18pt}{u(x) = 7x^2 + x ln(x)}$$ and $$style{font-size:18pt}{v(x) = x ln (x) -3x^2}$$.Let $$style{font-size:18pt}{y_1(x) = x^5}$$ be a solution of the corresponding homogeneous equation $$style{font-size:18pt}{Ly = 0.}$$(a) Write down a pair of linearly independent solutions of the homogeneous equation $$style{font-size:18pt}{Ly = 0.}$$ (b) Write down a solution of the non-homogeneous equation $$style{font-size:18pt}{Ly = f(x).}$$ (c) Write down the general solution of the non-homogeneous equation $$style{font-size:18pt}{Ly = f(x).}$$