Differential Equations

Question

How do we solve the equation,

y'(x) = y/(x*(ln(x)))

Answer 1

Integrating, we get:

ln(y) = ln(ln(x)) + C₁

e^ln(y) = e^{ln(ln(x)) + C1}

y = e^ln(ln(x))•e^C1

y = C₂• e^ln(ln(x))

y = C₂• ln(x)