# What is the general solution of the differential equation # xyy'=x^2+1 # ?

##### 1 Answer

Mar 23, 2017

# y^2 = x^2 + 2ln|x| + A #

#### Explanation:

The differential equation

# xyy'=x^2+1 #

is a First Order linear separable Differential Equation which can be solved simply by rearranging and collection term in

# ydy/dx = (x^2+1)/x #

And now we "separate the variables" to get;

# int \ y \ dy = int \ x+1/x \ dx#

Which is trivial to integrate to get:

# \ \ 1/2y^2 = 1/2x^2 + ln|x| + C #

# :. y^2 = x^2 + 2ln|x| + 2C #

# :. y^2 = x^2 + 2ln|x| + A #