Y(x) = x/(1+cx) ; dy/dx = y^2/x^2

[ziggie125]

Homework Statement

Show that each function in the family satisfies the differential equation.
y(x) = x/(1+cx) ; dy/dx = y^2/x^2

The Attempt at a Solution

I'm not sure where to start. I can't see how the integral of dy/dx = y(x)

 

[Coto]

Start by taking dy/dx of your y(x) equation, then compare that to y^2/x^2. What do you get?

 

[ziggie125]

thanks for the reply.

y(x) = x/(1+cx)

dy/dx = ((1+cx) - xc)/(1+cx)^2 = 1/(1+cx)^2

So how does that equal y^2/x^2

 

[D H]

What is y^2/x^2?

 

[ziggie125]

I'm not sure what you mean. This is all the information i was given for the problem.

 

[Coto]

You have solved dy/dx given that you had started with y(x). That is, you solved the left side of dy/dx = y^2/x^2. Now you have to solve the right side. y^2 = (y(x))^2, try plugging in y(x) to the RHS of that equation and see if the two match up.

 

[ziggie125]

Click, so you mean,

y^2/x^2 = 1/(1 cx)^2

y^2 = x^2/(1+cx)^2

sqrt(y^2) = sqrt(x^2/(1+cx)^2) = sqrt((x/(1+cx))^2))

y = x/(1+cx)

 

[Coto]

Yes :). But in this case it suffices to just show that y^2/x^2 is the same as dy/dx, which you did in the first step.

 

[ziggie125]

Alright. Thanks for the help, it is greatly appreciated.