- #1

Prof. 27

- 50

- 1

## Homework Statement

dv/dt = 9.8 - 0.196v

Set in correct form:

dv/dt + 0.196v = 9.8

Since p(t) = 0.196, u(t) the integration factor is given by:

u(t) = e

^{∫0.196 dt}

Multiply each term by u(t) and rearrange:

(e

^{∫0.196 dt})(dv/dt) + (0.196)(e

^{∫0.196 dt})(v) = (9.8)(e

^{∫0.196 dt})

From now on we will set e

^{∫0.196 dt}equal to D and leave it at that.

Here's where I no longer understand it. We take into consideration the product rule:

(f(x)*f(y))' = f'(x)f'(y) + f(x)f'(y)

Pauls' Online Notes gets:

(D*v)' = 9.8D

My question is, where did the 0.196 go? I don't see how he's justified in making p(t) just disappear.

## Homework Equations

(f(x)*f(y))' = f'(x)f'(y) + f(x)f'(y)

## The Attempt at a Solution

My Father who was a math major 30 years ago but went into business and has forgotten a lot

http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx

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