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Chapter 2: Q2E (page 64)

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

(x103-2y)dx+xdy=0.

Short Answer

Expert verified

The equation is linear.

Step by step solution

01

Find if the equation is separable

Here,

(x103-2y)dx+xdy=0dydx=2y-x103x

This equation cannot be written in the form as g(x) h(y).so, this equation is not Separable.

02

Determine if the equation is linear

The equation can be written as

dydx-2yx=-x103

Now,

P(x)=-2x,Q(x)=-x103

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)=x103-2yN(x,y)=x

鈭�M鈭�y=-2鈭�N鈭�x=1鈭�M鈭�y鈮�鈭�N鈭�x

This equation is not exact.

Hence, the equation is linear.

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