Solve for the initial value of the differential equation

[jpp46656]

Homework Statement

Solve the initial value problem: y+(3x-xy+2)dy/dx = 0 , y(1)=1

I couldn't separate with y as a dependent variable, so I made x the dependent variable and I get this: dx/dy= x(1-2/y)-(2/y),
in linear standard form: dx/dy+(3/y - 1)x = -2/y.

Homework Equations

The Attempt at a Solution

You can see that I attempted the solution. I'm just wondering if I performed the steps correctly and if the answer is correct.

 

[jpp46656]

Oh, and the work is shown in the pictures.

 

[haruspex]

I'm just wondering if I performed the steps correctly and if the answer is correct.

Did you try substituting the solution back into the given equations?