# What is a general solution to the differential equation #y'=5x^(2/3)y^4#?

##### 1 Answer

Nov 14, 2016

# y = root(3)(1/(C -9x^(5/3))) #

#### Explanation:

# dy/dx = 5x^(2/3)y^4 #

This is a First Order separable DE, so collecting like terms and "separating the variables" we get;

# int y^-4dy = int5x^(2/3) dx #

Integrating we get:

# y^-3/-3 = 5x^(5/3)/(5/3) + C_1 #

# y^-3 = -9x^(5/3) - 3C_1 #

# 1/y^3 = -9x^(5/3) + C #

# y^3 = 1/(C -9x^(5/3)) #

# y = root(3)(1/(C -9x^(5/3))) #