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 · 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 10336 views around the world You can reuse this answer Creative Commons License