   Chapter 3.3, Problem 53E

Chapter
Section
Textbook Problem

Find constants A and B such that the function y = A sin x + B cos x satisfies the differential equationy" + y' – 2y = sin x.

To determine

To find: The constants A and B.

Explanation

Given:

The function is y=Asinx+Bcosx.

The differential equation y+y2y=sinx.

Derivative Rules:

(1) Sum Rule: ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]

(2) Difference Rule: ddx[f(x)g(x)]=ddx[f(x)]ddx[g(x)]

Calculation:

Obtain the first derivative of y.

y=ddx(y)=ddx(Asinx+Bcosx)

Apply the sum rule (1),

Thus, the first derivative of y is y=AcosxBsinx.

Obtain the second derivative of y.

y=ddx(y)=ddx(AcosxBsinx)

Apply the difference rule (2),

Thus, the first derivative of y is y=AsinxBcosx

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Differentiate. J(v) = (v3 2v)(v4 + v2)

Single Variable Calculus: Early Transcendentals, Volume I

If f(x) 5 for all x [2, 6] then 26f(x)dx. (Choose the best answer.) a) 4 b) 5 c) 20 d) 30

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The graph of x = cos t, y = sin2 t is:

Study Guide for Stewart's Multivariable Calculus, 8th 