(1 point) 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
$$y' - \frac{5}{x}y = \frac{y^6}{x^9}$$,
and find the solution that satisfies y(1) = 1.
$$y(x) =$$
