Explanation Given: Population growth model for population changed either by immigrations d y d x = k y + f ( t ) , k = 0.02 y ( 0 ) = 10000 f ( t ) = − t Approach: General form of linear differential equation of first order is d y d x + P ( x ) y = Q ( x ) Steps to solve linear differential equation of first order are given below: Write given equation in standard form of first order differential equation. Find value of P ( x ) and Q ( x ) . Find integrating factor as I . F = e ∫ P ( x ) d x . Solution of first order linear differential equation is in the form as given below y × ( I . F ) = ∫ ( I . F ) × Q ( x ) d x + C Use initial condition to solve for value of C . Calculation: Given equation is d y d t = k y + f ( t ) and k = 0.02 y ( 0 ) = 10000 f ( t ) = − t We can rearrange equation as: d y d t = 0.02 y − t d y d t − 0.02 y = − t On comparing with d y d t + P ( t ) y = Q ( t ) P ( t ) = − 0.02 , Q ( t ) = − t Hence I . F = e ∫ − 0.02 d t = e − 0

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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 11.2, Problem 31E

To determine

To find:

The differential equation dydx=ky+f(t) which is subjected to initial condition y(0)=10000 for the function f(t)=−t.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.2, Problem 30E

Chapter 11.2, Problem 32E

Students have asked these similar questions

3. Determine the appropriate annihilator for the given F(x). a) F(x) = 5 cos 2x b) F(x)=9x2e3x

Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations).

Vectors u and v are shown on the graph.Part A: Write u and v in component form. Show your work. Part B: Find u + v. Show your work.Part C: Find 5u − 2v. Show your work.

Chapter 11 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 11.1 - YOUR TURN 1 Find all solutions of the differential...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - YOUR TURN In Example 6, find the goat population...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 2E Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E

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.

The differential equation d y d x = k y + f ( t ) which is subjected to initial condition y ( 0 ) = 10000 for the function f ( t ) = − t .

Solution Summary: The author explains how to solve a linear differential equation of first order.

Concept explainers

Videos

To find:

The differential equation dydx=ky+f(t) which is subjected to initial condition y(0)=10000 for the function f(t)=−t.

Want to see the full answer?

Chapter 11 Solutions

The differential equation d y d x = k y + f ( t ) which is subjected to initial condition y ( 0 ) = 10000 for the function f ( t ) = − t .

Solution Summary: The author explains how to solve a linear differential equation of first order.

Concept explainers

Videos

To find: The differential equation dydx=ky+f(t) which is subjected to initial condition y(0)=10000 for the function f(t)=−t.

Want to see the full answer?

Chapter 11 Solutions

To find:

The differential equation dydx=ky+f(t) which is subjected to initial condition y(0)=10000 for the function f(t)=−t.