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Chapter 8: Q 13-25MP (page 466)

Question: In Problemsto , find a particular solution satisfying the given conditions.

Short Answer

Expert verified

The solution of given differential equation is

Step by step solution

01

Given information.

The differential equation is .

02

Differential equation.

03

Find the solution of the given differential equation.

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Most popular questions from this chapter

Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example .

y+y/x2+1=1/(x+x2+1)

Use the methods of this section to solve the following differential equations. Compare computer solutions and reconcile differences.

y'=cos(x+y)

Hint: Let u=x+y; then u'=1+y'.

In Problem 33 to 38, solve the given differential equations by using the principle of superposition [see the solution of equation (6.29)]. For example, in Problem 33, solve three differential equations with right-hand sides equal to the three different brackets. Note that terms with the same exponential factor are kept together; thus, a polynomial of any degree is kept together in one bracket.

y"-2y'=9xe-x-6x2+4e2x

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.

2. x1-y2dx+y1-x2dy=0,y=12whenx=12

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

y"-6y'+9y=te3t,

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