Answer to Question #321298 in Differential Equations for Segun

Question

Solve the differential equation (x +4) dy/dx = x(y-3), given that y=4 when x= -3.

Answer 1

Solution

Given equation is separable differential equation. So

dy/(y-3) = xdx/(x+4)

dy/(y-3) = dx – 4dx/(x+4)

ln|y-3| = x – 4ln|x+4| + C

y-3 = e^xe^C/(x+4)⁴  

y = 3 + e^xe^C/(x+4)⁴  

If y=4 when x= -3 then 4 = 3 + e^C e^-3 => e^C = e³Â Â => y(x) = 3 + e^x+3/(x+4)⁴    

Answer

y(x) = 3 + e^x+3/(x+4)⁴