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Chapter 8: Q8-2-15P (page 398)

In problems 13 to 15, find a solution (or solutions) of the differential equation not obtainable by specializing the constant in your solution of the original problem. Hint: See Example 3

Problem 11

Short Answer

Expert verified

The solution is y=2.

Step by step solution

01

Given Information.

Differential Equation given is 2y'=3y-213

02

Definition of Differential equation

A differential equation is an equation that contains at least onederivativeof an unknown function, either an ordinary derivative or a partial derivative.

03

Solve differential equation

Separate the variables in problem 11 to get

dyy-213=32dx

The general solution of this differential equation is

y=x+C132+2

Now,dyy2is not valid for y=2

y=2 is a solution of this differential equation that cannot be obtained by any choice of C1

Therefore, the solution is y=2 .

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Most popular questions from this chapter

For each of the following differential equations, separate variables and find a solution containing one arbitrary constant. Then find the value of the constant to give a particular solution satisfying the given boundary condition. Computer plot a slope field and some of the solution curves.

3.y'sinx=ylny,y=ewhenx=蟺3

Solve the following sets of equations by the Laplace transform method

.y'+2z=1y0=02y-zz'=2tz0=1

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

y"+4y'+4y=e-2t,yv=0,尉0=4

In Problems 13 to 15, find a solution (or solutions) of the differential equation not obtainable by specializing the constant in your solution of the original problem. Hint: See Example 3.

13. Problem 2

Consider the differential equation (D-a)(D-b)y=Pn(x), where Pn(X)is a polynomial of degree n. Show that a particular solution of this equation is given by (6.24)with c=0; that is, ypis {apolynomialQnxofdegreenifaandbarebothdifferentfromzero;xQnxifa鈮�0,butb=0x2Qnxifa=b=0
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