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