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.

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Presentation transcript:

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.

Example Given y(0) = 1, find the particular solution of.

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

Example Find the general solution of.

Homework Pg 357 #1-10