Differential Equation, Separable, I believe

[Marylander]

Haven't done one of these in awhile and I was looking for a place to make sure I was doing it right. Hopefully one of you can take the time to look it over?

Homework Statement

Find the unique solution of the differential equation (3y^2)x(dy/dx)-x+1=0 for which y(e)=1

Homework Equations

None.

The Attempt at a Solution

(3y^2)dy=((x-1)/x)dx

Integrate

y^3=x-lnx+C

Substitute in for unique solution

1^3=e-ln(e)+C
2-e=C

 

[tiny-tim]

Welcome to PF!

Hi Marylander ! Welcome to PF!

(try using the X² tag just above the Reply box )

Find the unique solution of the differential equation (3y^2)x(dy/dx)-x+1=0 for which y(e)=1
…
(3y^2)dy=((x-1)/x)dx

Integrate

y^3=x-lnx+C

Substitute in for unique solution

1^3=e-ln(e)+C
2-e=C

Looks good!

 

[Marylander]

Didn't think to. Too used to not having it.

Good, thanks for checking.