- #1
Schaus
- 118
- 5
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+y6
##\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!
Last edited: