Separable Differential Equations Worksheets printable pdf download

Separable Differential Equations Worksheets

Calculus Maximus

Notes 5.1: Separable Diff EQ

§5.1—Separable Differential Equations

A differential equation is an equation that has one or more derivatives in it. The order of a differential

equation is the highest derivative present in the equation.

We know that antidifferentiation, indefinite integration, and solving differential equations all imply the

same process. The differential equations we’ve seen so far have been explicit functions of a single

 













variable, like

order) or

f x

sin

order) or even

h t

(second order).

 

Solving these equations meant getting back to either y  or

f x  or

h t  . The general solution

 . The particular solution required an initial condition and meant we had to find C .

meant C

A separable differential equation is one in which all x and dx ’s can be separated from all the y and dy ’s.

( )

= f x

g y

A first-order separable differential can be written in the form

, that is, as a PRODUCT

of x-factors and y-factors.

As you will see in the next section, this separation is not always easy or possible; however, in this section

we will focus on developing analytic methods for solving 1

order, separable differential equations.

For these types of problems, it is very, very, very important to SHOW THE SEPARATION OF THE

VARIABLES.

Example 1:

The graph of several solutions to the differential equation



is shown. Solve the equation, then find the

particular solution that satisfy the initial conditions

 

 , (b)

  , and (c)

 .

(a)

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Separable Differential Equations Worksheets

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