Chapter 2: Q1E (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.
$(x^{2} y + x^{4} \cos x) dx - x^{3} dy = 0$

Short Answer

Expert verified

The equation is linear.

Step by step solution

Find if the equation is separable

Here

$(x^{2} y + x^{4} \cos x) dx - x^{3} dy = 0 \frac{dy}{dx} = \frac{(x^{2} y + x^{4} \cos x)}{x^{3}}$

This equation cannot be written in the form as g(x) h(y).

so, this equation is not separable.

Determine if the equation is linear

The equation can be written as

$\frac{dy}{dx} - \frac{y}{x} = x \cos x$

Now, $P (x) = - \frac{1}{x}, Q (x) = x \cos x$

This equation is a linear.

Evaluate whether the equation is exact

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

$M (x, y) = x^{2} y + x^{4} \cos x N (x, y) = - x^{3}$

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

Hence, the equation is linear.

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In problems Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.
$(x^{2} y + x^{4} \cos x) dx - x^{3} dy = 0$

Short Answer

Step by step solution

Find if the equation is separable

Determine if the equation is linear

Evaluate whether the equation is exact

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Most popular questions from this chapter

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In problems Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.(x2y+x4cosx)dx-x3dy=0

Short Answer

Step by step solution

Find if the equation is separable

Determine if the equation is linear

Evaluate whether the equation is exact

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

Decision Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In problems Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.
$(x^{2} y + x^{4} \cos x) dx - x^{3} dy = 0$