- #1

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## Homework Statement

Solve for y: ##\frac {dy}{dx} = \frac {1+y^6}{xy^5}## , where y(1) = 1.

Answer ## y = \sqrt[6] {2x-1}##

## Homework Equations

## The Attempt at a Solution

##\frac {dy}{dx} = \frac {1+y^6}{xy^5}##

##\frac{dy (y^5)}{1+y^6} = dx \frac {1}{x}##

u= 1+y

^{6}

##\frac {du}{y^5}=dx##

##\int \frac{1}{u}du = \int \frac {1}{x}dx##

##\ln|1+y^6| = \ln|x| + C##

The natural logs cancel out.

Substituting in my (1,1)

## 1+1^6 = 0+C##

##C=2##

This is where I'm a bit lost. I'm not sure where I messed up but I don't know how to get the 2x-1. Any help would be greatly appreciated!

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