powers

**dankelly07** · February 13th 2008, 04:31 AM

Very quickly, if your taking powers across the other side eg deifferential equations, how does it work again, im having a blank!!!

eg
solving for y

-y^-5 = 6x+C

becomes

y = (6x+C)-1/5

IS this right??

If it is can anyone explain the thoery behind it???

**dankelly07** · February 13th 2008, 04:37 AM

ah man i think i wrote the question out wrong...

can anyone help me find the solution for the separable equation
6y^6

I already know the answer

for y(0)=3
(1/243 - 30x)^-(1/5)

but can anyone help me through the stages?
I just need explicit help with this solution, I keep going wrong with the basic Algebra i think

**vperera** · February 13th 2008, 04:41 AM

It should be y=(6x+C)^-(1/5).

Just multiply the exponent by its inverse (like if the exponent is 2, multiply both sides of the equation by 1/2).

**topsquark** · February 13th 2008, 04:46 AM

Originally Posted by dankelly07

can anyone help me find the solution for the separable equation
6y^6

This is not an equation. What is your original equation?

-Dan

**dankelly07** · February 13th 2008, 02:21 PM

sorry for the delayed reply,

The equation I asked to solve was

dy/dx = 6y^6

find the general solution
w/ condition y(0) = 3

**mr fantastic** · February 13th 2008, 03:19 PM

Originally Posted by dankelly07

sorry for the delayed reply,

The equation I asked to solve was

dy/dx = 6y^6

find the general solution
w/ condition y(0) = 3

$\frac{dx}{dy} = \frac{1}{6} \frac{1}{y^6} = \frac{1}{6} y^{-6}$ .

Therefore:

$x = \frac{1}{6} \left( \frac{-1}{5} \right) y^{-5} + C$

$= -\frac{1}{30} \frac{1}{y^5} + C$

$\Rightarrow 30(x - C) = \frac{1}{y^5}$ .

You know that when x = 0, y = 3:

$-30C = \frac{1}{3^5} = \frac{1}{243}$ .

Therefore $30x - \frac{1}{243} = \frac{1}{y^5}$ .

You can finish it off if you want to make y the subject .....

**dankelly07** · February 14th 2008, 06:20 AM

Yeah thats gr8, I cant see where I was going wrong, I'm v bad at factorising!

Thread: powers

LinkBack

Thread Tools

Display

powers

Similar Math Help Forum Discussions

Powers of Two

Powers

Sum of nth powers

powers of 2

Search Tags