Question

$$ \cos (x+y) d y=d x $$

Name: Problem 22, Chapter 2: Differential Equations
Uploaded: 2021-09-03T16:16:15-08:00
Duration: 4 min 5 s
Channel: Vishnu P
Description: cos(x+y) d y=d x

   $$
\cos (x+y) d y=d x
$$

Differential Equations

E. RUKMANGADACHARI 2012 Edition

Chapter 2, Problem 22

Instant Answer

Solved by Expert Vishnu P

09/03/2021

Step 1

Then, we can differentiate this with respect to $x$ to get $dv/dx = 1 + dy/dx$. Show more…

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$$ \cos (x+y) d y=d x $$

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Key Concepts

Ordinary Differential Equations

These equations involve an unknown function and its derivatives with respect to a single variable. They form the basis of modeling continuous phenomena in many fields, and techniques for solving them are central to mathematical analysis and applied mathematics.

Separation of Variables

This is a method used to solve differential equations by algebraically rearranging the equation so that each variable and its differential are on opposite sides of the equation. This allows each side to be integrated independently, leading to a solution.

Substitution Methods

Substitution methods involve introducing a new variable to simplify the structure of a differential equation. For example, combining terms by setting a new variable equal to a function of the existing variables can transform the equation into one that is more easily separable or integrable.

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