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6 Nov 2019
This is from "Elementary Differential Equations" by William E.Boyce and Richard C. DiPrima. It is in chapter 2, section 4. It isproblem number 22.
22. (a) Verify that both y1(t) = 1-t andy2(t) = -t2/4 are solutions of the initialvalue problem
y´ = (-t + (t2 + 4y)1/2) / 2, y(2) = -1.
Where are these solutions valid?
(b) Explain why the existence of two solutions of the givenproblem does not contradict the uniqueness part of Theorem2.4.2.
(c) Show that y = ct + c2, where c is an arbitraryconstant, satisfies the differential equation in part (a) for t> or equal to -2c. If c = -1, the initial condition is alsosatisfied, and the solution y = y1(t) is obtained. Showthat there is no choice of c that gives the second solution y =y2(t).
This is from "Elementary Differential Equations" by William E.Boyce and Richard C. DiPrima. It is in chapter 2, section 4. It isproblem number 22.
22. (a) Verify that both y1(t) = 1-t andy2(t) = -t2/4 are solutions of the initialvalue problem
y´ = (-t + (t2 + 4y)1/2) / 2, y(2) = -1.
Where are these solutions valid?
(b) Explain why the existence of two solutions of the givenproblem does not contradict the uniqueness part of Theorem2.4.2.
(c) Show that y = ct + c2, where c is an arbitraryconstant, satisfies the differential equation in part (a) for t> or equal to -2c. If c = -1, the initial condition is alsosatisfied, and the solution y = y1(t) is obtained. Showthat there is no choice of c that gives the second solution y =y2(t).
Trinidad TremblayLv2
18 Jan 2019
