Exponential Growth and Decay

6.4

Separation of Variables

When we have a first order differential equation which is implicitly defined, we can try to use a method called separation of variables to solve the equation.

Separation of Variables

Goal: get all y’s on one side (including dy) and all x’s on the other side (including dx).

Once I have done this I integrate each side with respect to the appropriate variable and solve for y.

Note: you MUST be multiplying each side by dy or dx. You cannot be adding, subtracting, or dividing.

Example

Find the particular solution to the equation given that y=1 when x=1.2( )

dyxy

dx

Example

Given y(0) = 1, find the particular solution of . 2 2 1 0xxydx e y dy

Example

Find the equation of the curve passing through (1, 3) that has a general slope of

.2y

x

Example

Find the general solution of . 2 4 dydxx xy

Homework

Pg 357 #1-10