Solve this differential equation using separation of variables

[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?

please help

 

[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.

 

[escobar147]

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.

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

 

[rock.freak667]

dy/dx = y² x

Divide both sides by y²

(1/y²)dy/dx = x

 

[escobar147]

dy/dx = y² x

Divide both sides by y²

(1/y²)dy/dx = x

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

 

[rock.freak667]

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

Well you can think of the 1 like that yes.