x*y = a(y+√(y²-x²)) then show that x³*dy/dx=y²(y+√(y²-x²)) ? Calculus Applications of Definite Integrals Solving Separable Differential Equations 1 Answer Cesareo R. Oct 1, 2016 dy/dx = (y^2)/(x^3)(y+sqrt(y^2-y^2)) Explanation: Making f(x,y) = (xy)/(y+sqrt(y^2-x^2))-a=0 we have df = f_x dx + f_y dy = 0 with f_x = y^2/(-x^2 + y (y + sqrt[-x^2 + y^2])) f_y = (x (y - sqrt[-x^2 + y^2]))/(x^2 - y (y + sqrt[-x^2 + y^2])) so dy/dx = -(f_x)/(f_y) = (y^2)/(x^3)(y+sqrt(y^2-y^2)) 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 3440 views around the world You can reuse this answer Creative Commons License