Short Answer

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 $\frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{\cos y + e^{y}}$ .

The statement is true.

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Step by Step Solution

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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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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

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 $\frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{\cos y + e^{y}}$ .

Step by Step Solution

Using the differential formula

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

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

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

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 $\sin y + e^{y} = x^{6} - x^{2} + x + 1$ is an implicit solution to $\frac{dy}{dx} = \frac{6 x^{5} - 2 x + 1}{\cos y + e^{y}}$ .