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Chapter 8: Q 13-28MP (page 466)

Question: In Problems 25to 28, find a particular solution satisfying the given conditions.

when x = 1

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.

When fand its derivatives are inserted into the equation, a solution is a function y = f(x) that solves the differential equation. The highest order of any derivative of the unknown function appearing in the equation is the order of a differential equation.

03

Find the solution of the given differential equation.

Consider the equation.

Suppose yy' = u then,

Substitute the values in above equation.

Integrate above equation.

Substitute yy' for u in above equation.

Integrate above equation.

Substitute 3 for y, 0 for y' and 1 for x in Equation (1).

Substitute 3 for y, 4 for c and 1 for x in Equation (2).

Substitute 4 for c and 5/2 for d in Equation (2).

Thus, the solution of given differential equation is .

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Most popular questions from this chapter

ydy+(xy2-8x)dx=0,y=3 when x=1.

Use the convolution integral to find the inverse transforms of:

1(p+a)(p+b)2

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'.

Suppose the rate at which bacteria in a culture grow is proportional to the number present at any time. Write and solve the differential equation for the number N of bacteria as a function of time t if there are N0bacteria when t=0. Again note that (except for a change of sign) this is the same differential equation and solution as in the preceding problems.

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.

14. Problem 8.
See all solutions

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