Question 16 Find a general solution to the given differential equation for t > 0. t^2y''(t) + 13ty'(t) + 35y(t) = 0. y(t) = c1e^(-5t) + c2e^(-7t) y(t) = e^(-5t)[c1cos(7ln(t)) + c2sin(7ln(t))] y(t) = c1t^(-5) + c2t^(-7) y(t) = e^(-5t)[c1cos(-7ln(t)) + c2sin(-7ln(t))] y(t) = c1t^5 + c2t^7 Question 16 Find a general solution to the given differential equation for t > 0. t^2y''(t) + 13ty'(t) + 35y(t) = 0 y = e^(-5t)[c1cos(7ln(t)) + c2sin(7ln(t))] y = c1t^5 + c2t
Added by Curtis W.
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Substitute y(t) = e^(rt) into the differential equation t^2y''(t) + 13ty'(t) + 35y(t) = 0 to get: t^2(r^2e^(rt)) + 13t(re^(rt)) + 35e^(rt) = 0 Show more…
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