- #1

november1992

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## Homework Statement

x[itex]\frac{dy}{dx}[/itex] = 4y

## Homework Equations

I'm not sure if there is a specific equation for these type of problems. My professor just says to separate the two different variables and then integrate them with respect to x.

## The Attempt at a Solution

[itex]\frac{1}{4y}[/itex] [itex]\frac{dy}{dx}[/itex] = [itex]\frac{1}{x}[/itex]

∫[itex]\frac{1}{4y}[/itex] [itex]\frac{dy}{dx}[/itex] dx =∫[itex]\frac{1}{x}[/itex] dx

left side:

∫[itex]\frac{1}{4y}[/itex] [itex]\frac{dy}{dx}[/itex] dx

u = y

du = [itex]\frac{dy}{dx}[/itex] dx

[itex]\frac{1}{4}[/itex]∫[itex]\frac{1}{u}[/itex]du

ln(4y) + [itex]C_{y}[/itex]

right side:

∫[itex]\frac{1}{x}[/itex] dx

ln(x) + [itex]C_{x}[/itex]

ln(4y) = ln(x) + C

Do i have to continue or could I just stop here?

4y = [itex]e^{x}[/itex] * [itex]e^{c}[/itex]

y = [itex]\frac{e}{4}^{x}[/itex] * [itex]\frac{e}{4}^{c}[/itex]

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