SOLUTION: Dy/dx= xy/2lny

Question 683952: Dy/dx= xy/2lny
Answer by jim_thompson5910(35256) (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 ))
RELATED QUESTIONS
find dy/dx e^xy-ex^3 =... (answered by venugopalramana)

if x+y=xy, then dy/dx... (answered by drk)

given: u = √(xy) solve:... (answered by richard1234)

dy/dx=ytanx (answered by solver91311)

Use implicit differentiation to find dy/dx: e^xy- ex^3 =... (answered by venugopalramana)

find dy/dx for x^2y - xy^2 = -6 at... (answered by solver91311)

Let xy = 20. Find dy/dt given that x = 10 and dx/dt =... (answered by Alan3354)

compute dy/dx if: (a) sin y = cos 2x (b) x + sin y =... (answered by Edwin McCravy)

Find the value of {{{(dy)/(dx)}}} when x= -1 and y= 1, given that {{{3x^2+4xy-xy^3 =... (answered by ikleyn)