- #1
mmekosh
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Homework Statement
Solve the differential equation: dy/dx=(y-y2)/x , for all x[tex]\neq[/tex] 0
Homework Equations
Integration by Parts: [tex]\int[/tex] u dv = u v - [tex]\int[/tex] v du
[tex]\int[/tex]lnx= 1/x + C
[tex]\int[/tex] (1/x) = lnx + C
dy/dx lnx = 1/x
dy/dx 1/x = lnx
The Attempt at a Solution
dy/(y-y2)=dx/x
[tex]\int[/tex] 1/(y-y2) dy = [tex]\int[/tex] 1/x dx
[tex]\int[/tex] (1/y)(1/(1-y))dy = lnx + C
(Integration by parts)
u=1/x dv=(1/(1-y))dy
du=lnydy v= -ln(1-y)dy
-lny / y + [tex]\int[/tex] lny ln(1-y) dy
And then if I continue and do integration by parts again, it just goes back to the original integral.