What is a solution to the differential equation dy/dx=(x+sinx)/(3y^2)? Calculus Applications of Definite Integrals Solving Separable Differential Equations 1 Answer Eddie Sep 4, 2016 y = root3 (x^2/2 - cos x +C) Explanation: This is separable y' = (x + sin x)/(3y^2) 3y^2 \ y' = x + sin x int 3y^2 \ y' \ dx = int x + sin x \ dx int 3y^2 \ dy = int x + sin x \ dx y^3 = x^2/2 - cos x +C y = root3 (x^2/2 - cos x +C) 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 4139 views around the world You can reuse this answer Creative Commons License