(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the differential equation: dy/dx=(y-y^{2})/x , for all x[tex]\neq[/tex] 0

2. Relevant 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

3. The attempt at a solution

dy/(y-y^{2})=dx/x

[tex]\int[/tex] 1/(y-y^{2}) 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Derivatives of integrals

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