Chapter 1: Q9RP (page 1)

Decide whether the statement made is True or False. The relation $x^{2} + y^{3} - e^{y} = 1$ is an implicit solution to $\frac{dy}{dx} = \frac{e^{y} - 2 x}{3 y^{2}}$ .

Short Answer

Expert verified

The statement is false.

Step by step solution

Using the differential formula

For the result use the differential formula $\frac{d}{dx} (x^{n}) = n x^{n - 1}$ and consider x and y as variable.

Differentiating x2+y3-ey=1 with respect to x.

The given statement is,

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

Since, this is the given differential equation, the given statement is false.

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Decide whether the statement made is True or False. The relation $x^{2} + y^{3} - e^{y} = 1$ is an implicit solution to $\frac{dy}{dx} = \frac{e^{y} - 2 x}{3 y^{2}}$ .

Short Answer

Step by step solution

Using the differential formula

Differentiating x2+y3-ey=1 with respect to x.

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Decide whether the statement made is True or False. The relation x2+y3-ey=1 is an implicit solution to dydx=ey-2x3y2.

Short Answer

Step by step solution

Using the differential formula

Differentiating x2+y3-ey=1 with respect to x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Pure Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Decide whether the statement made is True or False. The relation $x^{2} + y^{3} - e^{y} = 1$ is an implicit solution to $\frac{dy}{dx} = \frac{e^{y} - 2 x}{3 y^{2}}$ .