💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 23 Easy Difficulty

(a) Solve the differential equation $ y' = 2x \sqrt {1 - y^2}. $
(b) Solve the initial-value problem $ y' = 2x \sqrt {1 - y^2}, y(0) = 0, $ and graph the solution.
(c) Does the initial-value problem $ y' = 2x \sqrt {1 - y^2}, y(0) = 2, $ have a solution? Explain.

Answer

a) $\sin ^{-1} y=x^{2}+C$
b) $$\sin ^{-1} y=x^{2} \text { and } y=\sin \left(x^{2}\right) \text { for }-\sqrt{\pi / 2} \leq x \leq \sqrt{\pi / 2}$$
c) No since $C$ is undefined $y(x)$ does not have a particular solution at $y(0)=2$

Discussion

You must be signed in to discuss.

Video Transcript

we have way have asked two weeks on route one, minus y. It's far too easy. Division are one minus. Why? It's important to conditional Twix. Its knees sign in worse. Why equal to two index Esquire over to last. See? So this cancer sign it. Waas Why would it expired? Messy. We have got to be that IHS the given That is why I do it once. Joe therefore me sign and worse they know in Kuala zero last See if it is doing what I see and no sign in worst why will expire Therefore we have going well Science X s black This is answer part of the problem No, me Now I see the problem We are san worse people zero plasticity Oh, it is signing Waas One is equal to x Esquire plus Sinan waas too. So sense scientists too. As you know rial result see is undefined that ISI is undefined in its going this'll season undefined their phone y x has not solution at this is