The idea is here to have a implicit equation and take from both sides of the equation the differential and solve out of this the derivative
The derivative is the ratio of two differentials and can be thought of as a fraction : dy/dx
eqn = Dt[x*y^3 + Sin[x + y]] == Dt
note: (dx+dy) = d(x+y) ( a calculation rules of differentials (one of them))
Using Solve for getting dy and dy is not working ?
The desired expression must be dy/dx = .....