Home work Calculus II Separation of Variables?

Question

Show all work please √(x^2-9 ) dy/dx= 5x

Answer 1

  dy  =   5x/√x^2 -9

How do you solve this problem

First inspect the given equation

the derivative of x^2 whis is in denominator is 2x which is in numerator

so

  subsitute   X^ - 9  = t    we get   2xdx  = dt

   dy  = 5/2  dt/√t

   y  = 5/2  Ã¢ÂˆÂšt  (1/1/2)  =  5√t   = 5√x^2-9 +c