In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
$y=x \sin x \quad: \quad x y^{\prime}=y+x \sqrt{x^{2}-y^{2}}(x \neq 0$ and $x>y$ or $x<-y)$

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 9

Differential Equations

Section 2

Basic Concepts

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Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Video Transcript

mhm. The given differential equation is X. Y. Dash is equal to Y plus X. Underwrote X squared minus by square. We need to check whether the function why is equal to X. Cynics is a solution to this equation or not. So first of all letters obtained the first elevator that is very dash which will be called to cynics plus X. Because X let us substitute in the differential equation. The left hand side will become, it's multiplied with my dish which is cenex plus X. Because X. Opening the brackets we get X. Cynics plus X square cause X. Now let us check the right hand side. This will be equal to why is X in X plus X. Under root X squared minus Y squared will be X square sign square X. So writing the poster mastitis we can take X. Comin from the on the right side. And on the outside we get X square. Underwrote band minus sign square X. Now one minus sine squared. Theta is caused Martita and underwrote sign will give the final result as X in X plus excess square cause X. And this is equal to the left hand side, so we can conclude that the given function is a solution of the given differential equation.

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