Solving y'=(xy-y²)/x² using substitution

[sedaw]

Homework Statement

y`=(xy-y^2)/x^2

The Attempt at a Solution

y` = y/x -(y/x)^2

{y/x=z , y=zx , y`=z+xz`}

-z^2=x*dz/dx


-z^2dx = xdz


what`s next ?


TNX .

 

[Mark44]

Next is to move the -z^2 and x factors around so they are with, respectively, dz and dx. Then integrate.

 

[AUMathTutor]

To integrate that, you need your z's on one side and your x's on the other. Dividing through by x*z^2 should do the trick.

 

[sedaw]

can u write can't understand .

TNX .

 

[sedaw]

it`s o k .

TNX