Find the particular solution for the initial value problem given below. No:Date:34-ex +12x² - 6,yco)= 2, 4"o)=3

Answered: Image /qna-images/answer/02110170-006c-4465-b0ad-69e3c1e6046e.jpg

Answered: 24- ex +12x²-6,yc0)=2, yo)=3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

please see the image
q5
For the initial value proble %3D y(0) = 1, then y(2) = %3D %3D
Problem 3. A 400 gallon tank contains water into which 10 lbs of salt is dissolved. Salt water containing 3 lbs of salt per gallon is being pumped in at a rate of 4 gallons per minute, and the well mixed solution is being pumped out at the same rate. Let A(t) be the number of lbs of salt in the tank at time t in minutes. Derive the initial value problem governing A(t). Solve this IVP for A.
Give the exact solution of the Initial Value Problem у%3D х(у + х) — 2, y(0) = 2 %3D Show your outputs in terms of the following: 1. Paper computation and solution
A particular region has a rabbit population of 1600. Two foxes are introduced to control the population of rabbits. Following this, the number of rabbits decreases according to the formula R(t) = 1700 – Aekt. - where A and k are constants, and R(t) is the number of rabbits in the region t years after the introduction of the foxes. (a) Given that the population of rabbits drops by one quarter after 5 years, find the values of A and k. (b) Following this model, how long will it take for the rabbits to become extinct? Give your answer to two decimal places. (c) Let F(t) be the number of foxes in the region t years after their introduction. If dF = 0.7F(t), dt find the time at which the rate of decrease of the rabbit population is equal to the rate of increase of the fox population, correct to two decimal places. dR dF Hint. Note that and represent the rates of change of the rabbit and fox dt dt populations respectively. (d) Identify any problems with this model.
A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = x -2y, x(0) = 0, y' = 2x + y, y(0) = 4; x(t) = -4et sin 2t, y(t) = 4et cos 2t
number of people who will be infected by t = 12 days. 7. Assume we are considering the survival of whales and that if the number of whales falls below a minimum survival level m, the species will become extinct. Assume also that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that high a population level. a. Discuss the following model for the whale population dP dt = k(MP)(Pm) where P (t) denotes the whale population at time t and k is a positive constant. b. Graph dP/dt versus P and P versus t. Consider the cases in which the initial population P(0) = Po satisfies Po

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS