- #1
dooogle
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Homework Statement
solve
dy/dx=y+cos(x)y^2010
using variation of parameters/constant method
Homework Equations
The Attempt at a Solution
let z=1/(y^(n-1))=1/(y^(2009))
dz/dx=(dz/dy)(dy/dx)
dz/dy=-(n-1)*y^(-n)*dy/dx=-(2009*y^-2010)*(y+cos(x)y^2010)
=-2009(y^(-2009)+cos(x))
since z=y^(-2009)
=-2009(z+cos(x))
so dz/dx=-2009z-2009cos(x)
how do i separate the f(z) and f(x) to integrate?
also i need to do the equation by integrating factor but do not know what to take as the integrating factor since normally i rearange an equation into the form dy/dx+p(x)y=q(x)
and take e^int(p(x))dx as the integrating factor
thanks for your time
dooogle