help with differential equation, ASAP?

Question

can someone solve this for me??
"with a very easy detailed solution and instruction,."

dx + xlnx lny dy=0

it say find the general formula??
Variable separable LED??

pleas solve it as soon as possible, i need it in 3 and half hours,.



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thank you very much you will going to save my life if you can help me,.

Answer 1

dx + xln(x)ln(y)dy = 0
xln(x)ln(y)dy = - dx
ln(y)dy = - dx/(xln(x))
y(ln(y) - 1) = - ln(ln(x)) + ln(C)
y(1 - ln(y)) = ln(Cln(x))
e^y/y^y = Cln(x)
ln(x) = C(e/y)^y
x = e^(C(e/y)^y)

y in terms of x is transcendental.