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Solve the differential equation.$$\frac{d y}{d x}=2 x \sqrt{1-y^{2}}, \quad-1<y<1$$

$$y=\sin \left(x^{2}+C\right)$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 7

Integrals and Transcendental Functions

Section 2

Exponential Change and Separable Differential Equations

Functions

Trig Integrals

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:07

Solve the differential equ…

03:53

02:08

02:39

Solve the given differenti…

07:09

04:08

08:23

11:49

13:40

00:45

we want to Seoul this differential equation here. Well, first thing. Let's go ahead and move all of our white terms up to look spell. We would want to divide each side by the square root of one minus y square on the left That'll give us one over the square root of one minus y square. We'll have d y. And then if we multiply the DX over, we get to X d X. Now let's integrate. You decided this the left hand side and pretty sure that's arc sine. So this is Sy inverse of why is equal to and then to integrate two ex Well, that's going to be power rule. So we add one to the power it becomes like squared. Then we divide by its new power. So the two cancel out. So we just get X squared plus C Now, let's just take sign on each side of this. Since in the problem, they tell us we're restricted between why is even too negative one and one. We won't need to put any extra restrictions on this. Why is he too, my abs sine of X squared plus seats of this here would be our solution

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