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Chapter 6: Q. 51 (page 570)

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

dydx=x2-2y2,y(0)=8

Short Answer

Expert verified

On solving, we gety(x)=x3-6x+5123

Step by step solution

01

Step 1. Given information

Given expressiondydx=x2-2y2,y(0)=8

02

Using the variable separable method

Calculating, we get

鈭�y2dy=鈭�x2-2dxy33=13x3-2x+C1y3=x3-6x+Cy=x3-6x+C3

03

Substitute x=0y=8  and calculate

Calculating, we get

8=C3C=512y(x)=x3-6x+5123

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