A Bernoulli differential equation is one of the form 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
du/dx+(1−n)P(x)u=(1−n)Q(x).

Use an appropriate substitution to solve the equation
y′−(2/x)y=y^3/x^2,

and find the solution that satisfies y(1)=1.

y(x)=