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Chapter 2: Q8E (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.

胃dr+(3r-胃-1)d胃=0

Short Answer

Expert verified

The equation is linear.

Step by step solution

01

Find if the equation is separable

Here

胃dr+(3r-胃-1)d胃=0d胃dr=胃1+胃-3r

This equation can be written in the form as g () h(r). so, this equation is not separable.

02

Determine if the equation is linear

The equation can be written as

drd胃+3r胃=1+1胃

Now,P(x)=3胃,Q(x)=1+1胃

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(r,胃)=胃N(r,胃)=3r-胃-1鈭�M鈭�胃=1鈭�N鈭�r=3鈭�M鈭�y鈮�鈭�N鈭�x

This equation is not exact.

Hence, the equation is linear.

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