Chapter 8: Q-8-3-12P (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.
$\frac{dx}{dy} = cosy - xtany$

Short Answer

Expert verified

The general solution of the differential equations is $x = y \cos y + C \cos y$

Step by step solution

Step 1: Given Information.

The given differential equations is $\frac{d x}{d y} = \cos y - x \tan y$

Step 2: Meaning of the first-order differential equation.

A first-order differential equation is defined by two variables,xandy, and its functionf(x,y)is defined on anXY-plane region.

Find the general solution.

Write this differential equation to make it in the form $y^{'} + P y = Q$ , that is

$x^{'} + x \tan y = \cos y$

From eq. 3.4,

$I = \int \tan y d y = - \ln (\cos y) r^{I} = \frac{1}{\cos y}$

Find a solution for this differential equation

$x e^{I} = \int (\frac{1}{\cos y}) \cos y d y = y + C x = y \cos y + C \cos y$

Therefore, the general solution of the differential equations is $x = y \cos y + C \cos y$ .

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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.
$\frac{dx}{dy} = cosy - xtany$

Short Answer

Step by step solution

Step 1: Given Information.

Step 2: Meaning of the first-order differential equation.

Find the general solution.

One App. One Place for Learning.

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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.dxdy=cosy-xtany

Short Answer

Step by step solution

Step 1: Given Information.

Step 2: 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

Electricity and Magnetism

Turning Points in Physics

Geometrical and Physical Optics

Modern Physics

Translational Dynamics

Dynamics

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.
$\frac{dx}{dy} = cosy - xtany$