What is a solution to the differential equation dy/dx=(3y)/(2+x)? Calculus Applications of Definite Integrals Solving Separable Differential Equations 1 Answer Alexander ยท Eddie Jul 19, 2016 y = e^(3C)(2+x)^(3) = C(2+x)^(3) Explanation: This differential equation is separable. dy/(dx) = (3y)/(2+x) dy = (3y)/(2+x) dx 1/(3y) dy = 1/(2+x) dx int 1/(3y) dy = int 1/(2+x) dx 1/3 int 1/y dy = int 1/(2+x) dx 1/3 ln y = ln(2+x) + C ln y = 3[ln(2+x)+C] y = e^(3[ln(2+x)+C]) y = e^(3C)(2+x)^(3) y = color(red)(C)(2+x)^(3) [where C is generic constant] 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 10729 views around the world You can reuse this answer Creative Commons License