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

Find the particular solution to the initial value problem: (3xy - 4x - 1)dy + y(y - 2)dx = 0; when x=1, y=2

2. Relevant equations

dy + (p(x)y - q(x))dx = 0

e^(-∫p(x)dx) * (c + ∫e^(∫p(x)dx) * q(x)dx)

3. The attempt at a solution

Sorry if this is vague, but I just spent 30 min typing out the entire process only to have it deleted. This is where I got stuck:

p(y) = 3y - 4 / y(y - 2)

q(y) = 1 / y(y - 2)

x = [y^(1/2) / (y-2)^(1/2)] * (c + ∫dy/[y^(3/2) * (y - 2)^(1/2)])

I don't know how to do the remaining integral. I think it's partial fractions but the y^(3/2) is confusing me.

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# Differential Equation of Order 1

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