What is the particular solution to the differential equation dy/dx= 3(1+3y)/ (1+x)^2 with the initial condition y(-2)=0

Answer 1

dy/3(1 + 3y) = (1 + x)^-2dx

ln | 1 + 3y | = - 1/ (1 + x) + C

|3y+1| = C₁e^-1/(x+1)

5 = C₁/e. C₁ = 5e

|3y+1| = 5e^{-1/x+1 + 1} = 5e^x/(x+1)

y = [-5e^x/(x+1) - 1] / 3