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Chapter 6: Q. 37 (page 570)

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.

37.dydx=xy,y0=-1

Short Answer

Expert verified

The answer isyx=-e12x2

Step by step solution

01

Step 1. Given information

We have been givendydx=xy,y0=-1

02

Step 2. Solve using antidifferentiation and/or variable separable method.

The differential equation can be solved by applying variable separable method.

鈭�1ydy=鈭�xdxlny=12x2+Cy=e12x2+Cy=Ae12x2eC=A

Now put y0=-1,

-1=Ae1202-1=A

So, the answer isyx=-e12x2

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