# Global solution to inhomogeneous Bernoulli ODE

 P: 2 Hi everyone, I have an inhomogeneous Bernoulli type ODE given by $u'(t) = \kappa u(t) + \ell(t) u^{\gamma}(t) + v(t),\ \ \ u(T)=b>0,...(1)$ where $t\in[0,T],\ \ \gamma\in (0,1)$. My concern is that how to prove the existence and uniqueness of the solution u(t) for all $t\in [0,T] .$ Thanks very much.