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

solve differential equation

xdy + (xy+y-1)dx=0

2. Relevant equations

dy/dx + P(x)y = Q(x)

u = exp[int(P(x)] - integrating factor

exp[int(P(x))]*[dy/dx+P(x)y = Q(x)]

=> d/dx[P(x)]y = exp[int(P(x))]Q(x)

int[d/dx[P(x)]y = exp[int(P(x))]Q(x)]

solution is with respect to y.

3. The attempt at a solution

xdy = -(xy+y-1)dx

dy/dx = (1-y+xy)/x

dx/dy = x/(1-y+xy)

dx/dy = x-x/y+1/y

dx/dy - x + x/y = 1/y

I'm stuck here, I'm just not sure who to get the equation into a linear form where I could take the integrating factor and solve for x in the case since I switched the dependent variables to see if that wouldn't make it more complicated, any help from that point on would be greatly appreciated.

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# Homework Help: Solution of linear differential equation

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