Solve this differential equation using separation of variables

1. Apr 7, 2012

escobar147

Solve the following first order, ordinary differential equations using separation of variables:

dy/dx = y^2 x

subject to y=-1 when x=0

the correct answer is: y = -2/x^2 + 2

i cannot seem to get this answer, after i separate the variables and integrate both sides i get:

y^2 x^2/2

then if i plug the values in i get y = 0????

2. Apr 7, 2012

rock.freak667

When you separate the variables you should get

(1/y^2)dy = x dx

Integrating 1/y^2 wrt y will not give you y^2. Rewrite it as y^-2.

3. Apr 7, 2012

escobar147

hi, thanks foryour reply i appreciate it, but could you please explain why when you separate variables y^2 become 1/y^2?

4. Apr 7, 2012

rock.freak667

dy/dx = y2 x

Divide both sides by y2

(1/y2)dy/dx = x

5. Apr 7, 2012

escobar147

where has the 1 come from? is it the coefficiant of dy/dx?

6. Apr 7, 2012

rock.freak667

Well you can think of the 1 like that yes.