Solve the differential equation

Question

the product of 1/6x and dy/dx equals y times the square root of the quantity 3x squared - 1.

Answer 1

Assuming that the first item was 1/(6 x)   , this differential equation can be easily solved by the method of separation of variables.  

 

Rewrite it as :  dy/ y = 6x sqrt(3 x² -1)   dx

 

Integrate both sides

 

 ln(y ) =(2/3)   (3 x² -1)^3/2  +C  

 

Then y = A exp( (2/3) (3 x² -1)^3/2  )

 

Where A is a constant of integration