Differential equations for engineering

I need the final answer please

Verify by substitution that the given functions form a basis. Solve the given initial value problem y” + 18y’ +90y = 0, -** cos (3x), e-% sin (3x), y(0) = 1, y (0) = -9 Enclose arguments of functions in parentheses. For example, sin (29x). Use an asterisk. * to indicate multiplication. For example, 2* f (x).a*** (x+b) * (c**+ d), b * tan(a *) or e(*) * b. Q

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