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Chapter 6: Q. 6 (page 569)

Verify that y(x)=x+9is a solution of the initial-value problem dydx=12yand y(0)=3.

Short Answer

Expert verified

The solution of the given differential equation has been verified.

Step by step solution

01

Step 1. Given information:

The differential equation:dydx=12y

y(0)=3

The solution of this differential equationy(x)=x+9

02

Step  2. Verify the solution.

dydx=12y2ydy=dx

Now integrate both sides.

鈭�2ydy=鈭�dx2鈭�ydy=鈭�dx2.y22=x+cy2=x+cy=x+c

Now find cby substituting y(0)=3

3=0+c3=cc=9

So, the solution is:y(x)=x+9

Thus, the solution has been verified.

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Most popular questions from this chapter

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