Chapter 2: Q17E (page 64)

In Problems 9–20, determine whether the equation is exact.
If it is, then solve it.
$(\frac{1}{y}) dx - (3 y - \frac{x}{y^{2}}) dy = 0$

Short Answer

Expert verified

The equation is not exact.

Step by step solution

Evaluate whether the equation is exact

Here $(\frac{1}{y}) dx - (3 y - \frac{x}{y^{2}}) dy = 0$

The condition for exact is $\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$ .

$M (x, y) = (\frac{1}{y}) N (x, y) = (3 y - \frac{x}{y^{2}}) \frac{\partial M}{\partial y} = - \frac{1}{y^{2}} \frac{\partial N}{\partial x} = \frac{1}{y^{2}} \frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}$

Hence the equation is not exact.

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In Problems 9–20, determine whether the equation is exact.
If it is, then solve it.
$(\frac{1}{y}) dx - (3 y - \frac{x}{y^{2}}) dy = 0$

Short Answer

Step by step solution

Evaluate whether the equation is exact

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In Problems 9–20, determine whether the equation is exact.If it is, then solve it.1ydx-3y-xy2dy=0

Short Answer

Step by step solution

Evaluate whether the equation is exact

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 9–20, determine whether the equation is exact.
If it is, then solve it.
$(\frac{1}{y}) dx - (3 y - \frac{x}{y^{2}}) dy = 0$