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In Exercises $1-10,$ find the general solution to the exact differential equation.$$\frac{d y}{d x}=\frac{1}{\sqrt{1-x^{2}}}-\frac{1}{\sqrt{x}}$$

$$y=\sin ^{-1} x-2 \sqrt{x}+C$$

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 6

Differential Equations and Mathematical Modeling

Section 1

Slope Fields and Euler's Method

Differentiation

Integration Techniques

Differential Equations

Second-Order Differential Equations

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In Exercises $1-10,$ find …

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In Exercises $1-10,$ solve…

Find the general solution …

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Solving a Differential Equ…

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his problem. We're going to find the general solution to the exact differential equation. And we're just going to do this by integrating so in the whole of Dubai. DX is just why and then we have to recognize that when we have won over this word of one minus X squared that rings a bell that this is, we normally think of it as a derivative of arc sine. So we know that for integrating this than the integral of one over square of one minus X squared is ark science. We have our sign of X and then we have the ah, we have minus one over sort of X, and that is a derivative of ah, minus two squared of X. And I think the way that is easy to visualize minus one over Room X is as negative x to the negative 1/2 power. So if we want to integrate this, we just add one to the powers we're next to the 1/2 and then we add a two negative too, so that when we take the derivative, we are left with a negative X a negative 1/2. So we have our minus two Room X and then we can't forget about the possibility of Constance. We have plus C and then all together. That is our general solution.

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