What is a solution to the differential equation #dy/dx=(1+x)/(xy)# with y(1)=-4?

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Answer 1 · 2016-07-11T18:52:18

#implies y = - sqrt( 2ln x +2 x + 14)#

separable equation so separate

#dy/dx=(1+x)/(xy)#

#y dy/dx=(1+x)/(x)#

#y dy/dx=1/x+1 #

#int \ y \ dy/dx \ dx= int \ 1/x+1 \ dx#

#int \ y \ dy = int \ 1/x+1 \ dx#

#y^2 /2 = ln x + x + C#

#y = pm sqrt( 2ln x +2 x + C)#

#y(1) = -4#

#-4 =pm sqrt( 0 + 2 + C)#

#implies y = - sqrt( 2ln x +2 x + 14)#