First Order Differential Equations where a<x<b (Intial value?)

[kafuzz]

Hi, I'm having trouble understanding what to do when a First order equation has an inequality at the end of it.

For example : sqrt(y-x^2y)*dy/dx = -xy where -1<x<1

I've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant.

What do I do with the inequality? Is it an initial value problem?

 

[tiny-tim]

welcome to pf!

hi kafuzz! welcome to pf!

HI've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant.

your solution contains √(1 - x²) …

you'll probably find that if |x| > 1, you get a solution with √(x² - 1), or maybe some inverse trig function