Suppose $y_1(t) = 3t^2$ and $y_2(t) = 6$ are both solutions of the second order linear homogeneous equation $y'' + p(t)y' + q(t)y = 0$. Which of the following below is NOT guaranteed to also be a solution of the same equation? (check one) A. $y = 2$ B. $y = 3t^2 + 3$ C. $y = -1t^2$ D. $y = -1t^2 + 2$ E. $y = 0$ F. All of the above are solutions
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First, let's substitute y(t) = 3t into the equation y'' + p(t)y' + q(t)y = 0: (3t)'' + p(t)(3t)' + q(t)(3t) = 0 6 + 3p(t) + 9tq(t) = 0 Show more…
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