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

Answer 1

Ezekiel Alexander

#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)#

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Answer 2

Emma Aldridge

The solution to the given differential equation (\frac{dy}{dx} = \frac{1+x}{xy}) with the initial condition (y(1) = -4) is:

[y(x) = -\sqrt{2(x+1)}]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.