Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x , with initial condition y(1) = 1.

For this case we have the following difference equation:
 
 Applying separable variables we have:
 
 Integrating both sides we have:
 
 
 applying exponential to both sides:
 
 For y (1) = 1 we have:
 
 Thus, the particular solution is:
 
 Whose domain is all real.
 
 y = 0.2 * exp ((3/2) x ^ 2)
 Domain: all real numbers