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

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 9

Differential Equations

Section 2

Basic Concepts

Discussion

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Watch More Solved Questions in Chapter 9

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

the given differential equation is bye signed by plus cause by plus X. four multiplied with my dish is equal to why. Now we need to check whether the given function. Why minus because Y is equal to X. Is a solution to this equation or not? So letters obtained the first innovative of the solution it will be very dash minus. Now the differential of course is signed with a negative sign. So we get plus sign by multiply. Good bye dash. This is equal to one. So we can see from here we can divide as common and I left with one plus signed by is equal to one and therefore we get wide actually equal to one divided by one plus sign. Bye. Now let us substitute this in the differential equation and check the left inside first. This will become equal to buy sign by plus because right plus now the value of excess by minus caused by and this entire thing is multiplied with a rash. So let us write it as it is both. Let us simplify the value within the bracket caused by cancels out with minus caused by and taking by common. We can write by, signed by Plus one now multiplied with my dash, which is equal to one divided by one Plus signed by. So this track, it cancels out with the denominator and we are left with Y, which is equal to the right hand side. So we can conclude that the given function this is a solution of the given differential equation.

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