Explanation Consider y = f ( x ) . That is, y = f ( x ) = C 1 e − 2 x + C 2 x e − 2 x . Differentiate the function y with respect to x . y ′ = f ′ ( x ) = d d x ( C 1 e − 2 x + x C 2 e − 2 x ) = C 1 e − 2 x ( − 2 ) + ( 1 ) C 2 e − 2 x + x C 2 e − 2 x ( − 2 ) [ ∵ d d x ( x n ) = n x n − 1 and ( u v ) ′ = u ′ v + u v ′ ] = − 2 C 1 e − 2 x + C 2 e − 2 x − 2 x C 2 e − 2 x Now, differentiate y ′ with respect to x . y ″ = f ″ ( x ) = d d x ( − 2 C 1 e − 2 x + C 2 e − 2 x − 2 x C 2 e − 2 x ) = − 2 C 1 e − 2 x ( − 2 ) + C 2 e − 2 x ( − 2 ) − 2 ( 1 ⋅ C 2 e − 2 x + x C 2 e − 2 x ( − 2 ) ) = 4 C 1 e − 2 x − 2 C 2 e − 2 x − 2 C 2 e − 2 x + 4 x C 2 e − 2 x Now substitute y = C 1 e − 2 x + C 2 x e − 2 x , y ′ = − 2 C 1 e − 2 x + C 2 e − 2 x − 2 x C 2 e − 2 x

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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 9.1, Problem 7E

To determine

To verify: The solution of the differential equation y″+4y′+4y=0 is y=C1e−2x+C2xe−2x.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 6E

Chapter 9.1, Problem 8E

Students have asked these similar questions

Let a = (-1, -2, -3) and 6 = (-4, 0, 1). Find the component of b onto a.

Forces of 9 pounds and 15 pounds act on each other with an angle of 72°. The magnitude of the resultant force The resultant force has an angle of pounds. * with the 9 pound force. The resultant force has an angle of with the 15 pound force. It is best to calculate each angle separately and check by seeing if they add to 72°.

= Let (6,2,-5) and = (5,4, -6). Compute the following: บี.บี. บี. นี = 2 −4(u. v) = (-4). v= ū. (-40) (ū. v) v =

Chapter 9 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 9.1 - Prob. 1CQ Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Prob. 3CQ Ch. 9.1 - Prob. 4CQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E

Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - SUPPLY AND DEMAND Let S(t) denote the supply of a...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - AMOUNT OF GLUCOSE IN THE BLOODSTREAM Suppose...Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - GOMPERTZ GROWTH CURVE Suppose a quantity Q(t) does...Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.2 - Prob. 1CQ Ch. 9.2 - Prob. 2CQ Ch. 9.2 - Prob. 3CQ Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - In Exercises 116, solve the first-order...Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.3 - Prob. 1CQ Ch. 9.3 - Prob. 2CQ Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - NEWTONS LAW OF COOLING Newtons Law of Cooling...Ch. 9.3 - Prob. 9E Ch. 9.3 - EXPONENTAL DECAY A radioactive isotope with an...Ch. 9.3 - RADIOACTIVE DECAY If 4 g of a radioactive...Ch. 9.3 - LEARNING CURVES The American Court Reporter...Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - SINKING FUNDS The proprietor of Carson Hardware...Ch. 9.3 - Prob. 19E Ch. 9.3 - GROWTH OF A FRUIT FLY COLONY A biologist has...Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Von Bertalanffy Growth Model The von Bertalanffy...Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - MIXTURE PROBLEMS A tank initially contains 50 gal...Ch. 9.4 - Prob. 1CQ Ch. 9.4 - Prob. 2CQ Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9 - Prob. 1CRQ Ch. 9 - Prob. 2CRQ Ch. 9 - Prob. 3CRQ Ch. 9 - Prob. 4CRQ Ch. 9 - Prob. 5CRQ Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - RESALE VALUE OF A MACHINE The resale value of a...Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 1BM Ch. 9 - Prob. 2BM Ch. 9 - Prob. 3BM Ch. 9 - Prob. 4BM

Knowledge Booster

$Calculus$

Learn more about

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

To verify: The solution of the differential equation y ″ + 4 y ′ + 4 y = 0 is y = C 1 e − 2 x + C 2 x e − 2 x .

Solution Summary: The author explains that the solution of the differential equation y′′+4

Concept explainers

Videos

To verify: The solution of the differential equation y″+4y′+4y=0 is y=C1e−2x+C2xe−2x.

Want to see the full answer?

Chapter 9 Solutions