SOLUTION: Dy/dx= xy/2lny

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Question 683952: Dy/dx= xy/2lny
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
dy/dx= xy/2lny

dy= xy/2lny*dx

2ln(y)/y*dy= x*dx

int(2ln(y)/y*dy)= int(x*dx)

2*int(ln(y)/y*dy)= int(x*dx)

2*((1/2)*ln(|y|)^2)= (1/2)x^2 + C

ln(|y|)^2= (1/2)x^2 + C

ln(|y|)= sqrt( (1/2)x^2 + C )

ln(|y|) = sqrt( (1/2)x^2 + C )

|y| = e^(sqrt( (1/2)x^2 + C ))

y = +-e^(sqrt( (1/2)x^2 + C ))