I have this Stochastic Differential Equation $$X_t=x+\int_0^t(\lambda X_s-X_s^2) \, ds+\int_0^t \sigma X_s W_s$$ with $x,σ,λ>0$ and $ W_t$ a brownian motion
I considered it as a stochastic differential equation with linear diffusion coefficient and I tried to use the integrating factor
$Y_{t}^{-1}=\exp\{-σW_t+\frac{1}{2}σ^2 t\}$ so the process
$Z_t:=X_t Y_t$ justifies the
$$dZ_t=Y_t^{-1}(λΥ_t Z_t-(\text{Υ}_t Z_t)^2) \, dt$$
$dZ_t=(λZ_t-Υ_t Z_t^2) \, dt$ but I don't know how to solve this