Match the solution curve with one of the differential equations. Where y" + 2y' + 2y = 0 y" + y = 0 y" + 16y = 0 y" + 2y' + y = 0 y" - 3y' 4y = 0 Oy" - 6y' + 8y = 0 Explain your reasoning. (Assume that k, k₁, and Kk₂ are all positive.) The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex (C₁ cos(x) + C₂ sin(x)). The auxiliary equation should have two positive roots, so that the solution has the form c₁ek1x + c₂ek2x. The auxiliary equation should have one positive and one negative root, so that the solution has the form c₁ek₁x + ₂е-k₂. e-kx + c₂xe-kx. The auxiliary equation should have a repeated negative root, so that the solution has the form c₁e The differential equation should have the form y" + k²y = 0 where k = 1 so that the period of the solution is 2π. k²y The differential equation should have the form y" + = 0 where k = 2 so that the period of the solution is 7.

Q: 0. Compute the exact values of the roots of the auxiliary equation, and construct the solution of…

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A: Topic- differential equations

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