What is a solution to the differential equation dy/dx = 1 - 0.2y? Calculus Applications of Definite Integrals Solving Separable Differential Equations 1 Answer Eddie Jul 2, 2016 y = alpha e^ (- 1/5 x) + 5 Explanation: dy/dx = 1 - 0.2y = 1/5 (5 - y) int 1/(5 - y) dy = 1/5 int dx int 1/(y-5) dy = -1/5 int dx ln(y-5) = - 1/5 x + C y-5 = exp (- 1/5 x + C) = alpha e^ (- 1/5 x) [where alpha = e^C] y = alpha e^ (- 1/5 x) + 5 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 5286 views around the world You can reuse this answer Creative Commons License