Chapter 8: Q5P (page 403)

Using $(3.9)$ , find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after $(3.9)$ , and Example 1.
$y' c o s x + y = c o s^{2} x$

Short Answer

Expert verified

Answer:

The general solution of the differential equation is $y = \frac{x - \cos (x) + C}{s e x (x) + \tan (x)}$ .

Step by step solution

Given information

The given differential equation is $y' \cos x + y = \cos^{2} x$ .

Meaning of the first-order differential equation

A first-order differential equation is defined by two variables, x and y, and its function $f (x, y)$ is defined on an XY-plane region.

Find the general solution

Write this differential equation to make it in the form $y' + P y = Q$ ; that is

$y' + y s e c (x) = \cos (x)$

From equation 3.4,

$I = \int s e c (x) d x = I n [s e c (x) + \tan (x)] e^{I} = e^{I n [s e c (x) + \tan (x)]} = s e c (x) + \tan (x)$ .

Find a solution for this differential equation.

Therefore, the general solution of the differential equation is.

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Using $(3.9)$ , find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after $(3.9)$ , and Example 1.
$y' c o s x + y = c o s^{2} x$

Short Answer

Step by step solution

Given information

Meaning of the first-order differential equation

Find the general solution

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Most popular questions from this chapter

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Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example 1.y'cosx+y=cos2x

Short Answer

Step by step solution

Given information

Meaning of the first-order differential equation

Find the general solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Geometrical and Physical Optics

Electromagnetism

Physics of Motion

Thermodynamics

Astrophysics

Study anywhere. Anytime. Across all devices.

Using $(3.9)$ , find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after $(3.9)$ , and Example 1.
$y' c o s x + y = c o s^{2} x$