# Question #ea738

Sep 21, 2016

$y = \frac{3 x}{2} + \frac{C}{x}$

#### Explanation:

$x y ' + y = 3 x$

the LHS of this equation is in exact form, ie $\frac{d}{\mathrm{dx}} \left(x y\right) = x y ' + y$

so we write it as
$\frac{d}{\mathrm{dx}} \left(x y\right) = 3 x$

and then we integrate the equation wrt x
$\int \left(\frac{d}{\mathrm{dx}} \left(x y\right) = 3 x\right) \mathrm{dx}$

$\int \frac{d}{\mathrm{dx}} \left(x y\right) \mathrm{dx} = \int 3 x \setminus \mathrm{dx}$

$\implies x y = \frac{3 {x}^{2}}{2} + C$

$y = \frac{3 x}{2} + \frac{C}{x}$