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## Homework Statement

If a = 9-v² then prove that v = 3 (e^6t - 1)/(e^6t + 1) the condition when t=0 also v has zero value

## Homework Equations

I don't quite understand in this but general equation should be dv/dt = a

## The Attempt at a Solution

Actually i don't don't have any idea in this problem since i only encountered something similar problem like determine v when a=v+1 or a=-bv² where b is coefficient but well i have gist since the final form is including euler number so natural logaritm should have something to do in this for me i write like this

dv/dt = a

dv/dt = 9-v²

dv/(9-v²) = dt since the only way I am know to attain answer that contain e is do something abou ln and go to form

dy/y = ln y

v² need become positive so

both sides multipled by -1

dv/(v²-9)=-dt (im I am sorry idont have integrer symbol so i will write it as intg)

dv/(v+3)(v-3) = -dt just from here I am not sure when forced its become like

then both side integrated so it become like ln (v+3) (v-3) = -t + C then i don't know anymore (frankly even this part I am not sure whether its i correct or just my foolishness) so please help I am really restless until i can solve this

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