# Thread: DE by Separation of Variables

1. ## DE by Separation of Variables

I just don't get this, could someone help me out?

Solve the given differential equations by separation of variables.

a) dy/dx=(x+1)^2

b) (e^x)y dy/dx= (e^-y) + (e^-2x-y)

thank you so much for your help

2. Originally Posted by kithy
I just don't get this, could someone help me out?

Solve the given differential equations by separation of variables.

a) dy/dx=(x+1)^2

b) (e^x)y dy/dx= (e^-y) + (e^-2x-y)

thank you so much for your help
I will do the first one and you can post some work on the second

$\displaystyle \frac{dy}{dx}=(x+1)^2$

Now by seperating variables we get

$\displaystyle dy=(x+1)^2dx$

Remaining inequality we have

$\displaystyle \int{dy}=\int(x+1)^2dx\Rightarrow{y=\frac{(x+1)^3} {3}+C}$

Where C is an arbitrary constant

Do you see it now for the second one?

3. In order to solve these equations, you need to separate the two variables to different sides of the equation along with their respective differentials (the dy or dx, you can move them around like any other number or variable). That's why they're called "separable" diff eqs. Mathstud showed you how to do it for the first problem. You follow the same path for solving the second one.