Select a function from below options so that if both sides of the equation is multiplied by the function, then the new ODE is exact.

Question

y^2*dx+ (xy+1) dy=0 is

Select a function from below options so that if both sides of the equation is multiplied by the function, then the new ODE is exact.

a.) y^(-2)

b.) x

c.) y^(-1)

d.) x/y

Please help

Answer 1

(c) y^-1(y2 dx+(xy+1)dy= ydx+xdy+y^-1dy=d(xy)+d(ln(y))=d(xy+ln(y))