# How do you solve the differential #dy/dx=(x-4)/sqrt(x^2-8x+1)#?

##### 1 Answer

Jan 10, 2017

# y = sqrt(x^2-8x+1) + C #

#### Explanation:

#d y/dx=(x-4)/sqrt(x^2-8x+1) #

Is a First Order separable DE which we can sole by integrating:

# :. y = int \ (x-4)/sqrt(x^2-8x+1) \ dx #

Let

Substituting into the RHS integral we get:

# y = int \ (1/2)/sqrt(u) \ du #

# \ \ = 1/2 int \ u^(-1/2) \ du #

# \ \ = 1/2 u^(1/2)/(1/2) + C#

# \ \ = sqrt(u) + C #

# \ \ = sqrt(x^2-8x+1) + C #

which is the General Solution