By using the substitution y=vx, show that the general solution of the first order homogeneous differential equation (x+y)[dy/dx]= y-x in the case where x>0 is given by y=k, where k is a constant.
By using the substitution y=vx, show that the general solution of the first order homogeneous differential equation (x+y)[dy/dx]= y-x in the case where x>0 is given by y=k, where k is a constant.
Many thanks in advance!
Okay, have you tried this at all? You can write the given equation as (x+y)dy= (y- x)dx. If y= vx, then dy= v dx+ x dv. Replace dy with that and replace y with xv and see what you get!
Far better to do it yourself than have someone do it for you.
I've checked the question with my instructor. Yea, the question has problems. It's the book's publisher's mistake. Thanks anyway. Good thing I got the general solution right.