Explanation Procedure used: General solution to differential equation subjected to boundary conditions: 1. Consider the differential equation L and find the roots of auxiliary equation f ( m ) . 2. Find the general solution. 3. Substitute the boundary values to determine the unknown coefficients. 4. Substitute the coefficients into the general solution. Calculation: Consider the differential equation y ″ + 2 y ′ + y = 0 and the auxiliary equation associated to y ″ + 2 y ′ + y = 0 is m 2 + 2 m + 1 = 0 . Calculate the roots of m 2 + 2 m + 1 = 0 with the help of m = ( − b ) ± b 2 − 4 a c 2 ( a ) . m = ( − 2 ) ± ( 2 ) 2 − 4 ( 1 ) ( 1 ) 2 ( 1 ) = − 2 ± 0 2 = − 1 ( twice ) Hence, the roots of the auxiliary equation are m 1 = − 1 and m 2 = − 1 . Both the roots are equal and repeated. Hence, the general solution is, y = c 1 e − x + c 2 x e − x Consider the boundary conditions y ( − 1 ) = 0 and y ′ ( 0 ) = 0

11th Edition

ISBN: 9781337652476

Author: ZILL

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 4, Problem 40RE

To determine

To solve: The differential equation y″+2y′+y=0 subjected to the boundary conditions y(−1)=0,y′(0)=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 39RE

Chapter 4, Problem 41RE

Students have asked these similar questions

Why the character no change for my remark?

Determine the radius of convergence of a power series:12.6.5, 12.6.6, 12.6.7, 12.6.8Hint: Use Theorem12.5.1 and root test, ratio test, integral test

In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $31 per doll. During the holiday selling season, FTC will sell the dolls for $39 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision. (a) Determine the equation for computing FTC's profit for given values of the…

Chapter 4 Solutions

FIRST COURSE IN DIFF.EQ.-WEBASSIGN

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Given that x(t) = c1 cos t + c2 sin t is the...Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The differential equation y ″ + 2 y ′ + y = 0 subjected to the boundary conditions y ( − 1 ) = 0 , y ′ ( 0 ) = 0 .

Solution Summary: The author explains the general solution of the differential equation subjected to boundary conditions.

Concept explainers

Videos

To solve: The differential equation y″+2y′+y=0 subjected to the boundary conditions y(−1)=0,y′(0)=0.

Want to see the full answer?

Chapter 4 Solutions