Match the solution curve with one of the differential equations. O y" + 4y = 0 O y" + 2y' + y = 0 O y" + y = 0 O y" – 2y' – 3y = 0 О у" - 7y' + 12y %3D 0 O y" + 2y' + 2y = 0 Explain your reasoning. (Assume that k, k1, and k2 are all positive.) O The auxiliary equation should have a repeated negative root, so that the solution has the form cje-kx + c2xe-kx. O The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form ex(cị cos ßx + c2 sin ß> O The differential equation should have the form y" + k2y = 0 where k = 1, so that the period of the solution is 27. O The auxiliary equation should have one positive and one negative root, so that the solution has the form czekix + cze¬k2x. O The differential equation should have the form y" + k2y = 0 where k = 2, so that the period of the solution is n. O The auxiliary equation should have two positive roots, so that the solution has the form cjek1X + c>ek2*.