Question

Question #ea738

Answer 1

`y = (3 x) /2 + C/x`

Explanation:

`x y' + y = 3x`

the LHS of this equation is in exact form, ie `d/dx (xy) = xy' + y`

so we write it as
`d/dx (xy) = 3x`

and then we integrate the equation wrt x
`int ( d/dx (xy) = 3x )dx`

`int d/dx (xy) dx = int 3x \ dx`

`implies xy = (3 x^2) /2 + C`

`y = (3 x) /2 + C/x`