Given x^t * y^m - (x+y)^(m+t)=0 determine dy/dx ? Calculus Applications of Definite Integrals Solving Separable Differential Equations 1 Answer Cesareo R. Oct 28, 2016 See below. Explanation: f(x,y)=x^t * y^m - (x+y)^(m+t)=0 df = f_xdx+f_ydy=0 so dy/dx=-f_x/(f_y) but f_x=t/x x^ty^m-(t+m)/(x+y)(x+y)^(t+m) and f_y=m/y x^ty^m-(t+m)/(x+y)(x+y)^(t+m) but x^ty^m=(x+y)^(t+m) then f_x=(t/x-(t+m)/(x+y))x^ty^m and f_y=(m/y-(t+m)/(x+y))x^ty^m so dy/dx=-(t/x - (t + m)/(x + y))/(m/y - (t + m)/(x + y))=y/x Answer link Related questions How do you solve separable differential equations? How do you solve separable first-order differential equations? How do you solve separable differential equations with initial conditions? What are separable differential equations? How do you solve the differential equation dy/dx=6y^2x, where y(1)=1/25 ? How do you solve the differential equation y'=e^(-y)(2x-4), where y5)=0 ? How do you solve the differential equation (dy)/dx=e^(y-x)sec(y)(1+x^2), where y(0)=0 ? How do I solve the equation dy/dt = 2y - 10? Given the general solution to t^2y'' - 4ty' + 4y = 0 is y= c_1t + c_2t^4, how do I solve the... How do I solve the differential equation xy'-y=3xy, y_1=0? See all questions in Solving Separable Differential Equations Impact of this question 1483 views around the world You can reuse this answer Creative Commons License