1. powers

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???

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

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

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

3. 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).

4. 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

5. 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

6. 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 .....

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