(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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.

3. 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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: First order separable differential equation

**Physics Forums | Science Articles, Homework Help, Discussion**