Answer to Question #262967 in Differential Equations for Neilmar

Question

Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

x dy/dx + y = 1/y^2

Answer 1

divide left and right sides of equation by $-(1-y^3)/y^2$ :

$\frac{y^2}{y^3-1}dy=-\frac{dx}{x}$

$\int\frac{y^2}{y^3-1}dy=-\int\frac{dx}{x}$

$\frac{ln(y^3-1)}{3}=c-lnx$

$y=\sqrt[3]{\frac{c_1}{x^3}+1}$