A Bernoulli differential equation is one of the form $$\frac{dy}{dx} + P(x)y = Q(x)y^n.$$
Observe that, if $n=0$ or $1$, the Bernoulli equation is linear. For other values of $n$, the substitution $u=y^{1-n}$ transforms the Bernoulli equation into the linear equation $$\frac{du}{dx} + (1-n)P(x)u = (1-n)Q(x).$$

Use an appropriate substitution to solve the equation $$y' - \frac{3}{x} y = \frac{y^4}{x^{3}},$$
and find the solution that satisfies $y(1)=1.$

$y(x) =$ .