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Chapter 2: Q5E (page 64)

In problems 1-8 Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.

xydx+dy=0

Short Answer

Expert verified

The equation is separable and also linear.

Step by step solution

01

Find if the equation is separable

Here

xydx+dy=0dydx=-xy

This equation can be written in the form as g(x) h(y).so, this equation is Separable.

02

Determine if the equation is linear

The equation can be written as

dydx+xy=0

Now,P(x)=x,Q(x)=0

This equation is a linear.

03

Evaluate whether the equation is exact

The condition for exact is鈭�M鈭�y=鈭�N鈭�x .

M(x,y)=xyN(x,y)=1鈭�M鈭�y=x鈭�N鈭�x=0鈭�M鈭�y鈮�鈭�N鈭�x

This equation is not exact.

Hence, the equation is separable and also linear.

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Most popular questions from this chapter

In problem 7-16, solve the equation.dydx=sec2y1+x2

Question: Use the substitution v=x-y+2 to solve equation (8).

dydx=y-x-1+x-y+2-1

Question: In Problems 1-30, solve the equation.

鈥�x2-2y-3dy+2xy-3x2dx=0

Question: In Problems 1-30, solve the equation.

dydx=x-y-1x+y+5

Question: In Problems 1-30, solve the equation.

dydx=2x+y-12
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