Chapter 1: Q10RP (page 1)

Decide whether the statement made is True or False. The relation $\sin y + e^{y} = x^{6} - x^{2} + x + 1$ is an implicit solution to $\frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{\cos y + e^{y}}$ .

Short Answer

Expert verified

The statement is true.

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 sin y+ey=x6-x2+x+1 with respect to x.

The Solution is given below,

$\frac{d}{dx} (\sin y + e^{y}) = \frac{d}{dx} (x^{6} - x^{2} + x + 1) cosy \frac{dy}{dx} + e^{y} \frac{dy}{dx} = 6 x^{5} - 2 x + 1 (cosy + e^{y}) \frac{dy}{dx} = 6 x^{5} - 2 x + 1 \frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{cosy + e^{y}}$

Hence, this is the given differential equation, the given statement is true.

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Decide whether the statement made is True or False. The relation $\sin y + e^{y} = x^{6} - x^{2} + x + 1$ is an implicit solution to $\frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{\cos y + e^{y}}$ .

Short Answer

Step by step solution

Using the differential formula

Differentiating sin y+ey=x6-x2+x+1 with respect to x.

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Decide whether the statement made is True or False. The relation siny+ey=x6-x2+x+1 is an implicit solution to dydx=6x5-2x+1cosy+ey.

Short Answer

Step by step solution

Using the differential formula

Differentiating sin y+ey=x6-x2+x+1 with respect to x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Applied Mathematics

Probability and Statistics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Decide whether the statement made is True or False. The relation $\sin y + e^{y} = x^{6} - x^{2} + x + 1$ is an implicit solution to $\frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{\cos y + e^{y}}$ .