Chapter 6: Q. 49 (page 570)

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29-52.
$\frac{d y}{d x} = y^{2} \cos x, y (π) = 1$

Short Answer

Expert verified

On solving, we get $y (x) = \frac{1}{1 - \sin x}$

Step by step solution

Step 1. Given information

Given expression $\frac{d y}{d x} = y^{2} \cos x, y (π) = 1$

Use the variable separable method

Calculating, we get

$\frac{d y}{d x} = y^{2} \cos x \frac{d y}{y^{2}} = \cos x d x - \frac{1}{y} = \sin x + C y = - \frac{1}{\sin x + C}$

Substitute x=πy=1 and calculate

Calculating, we get

$1 = - \frac{1}{0 + C} C = - 1 y (x) = \frac{1}{1 - \sin x}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29-52.
$\frac{d y}{d x} = y^{2} \cos x, y (π) = 1$

Short Answer

Step by step solution

Step 1. Given information

Use the variable separable method

Substitute x=πy=1 and calculate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Statistics

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29-52.dydx=y2cosx,y(π)=1

Short Answer

Step by step solution

Step 1. Given information

Use the variable separable method

Substitute x=πy=1 and calculate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Statistics

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29-52.
$\frac{d y}{d x} = y^{2} \cos x, y (π) = 1$