# Global solution to inhomogeneous Bernoulli ODE

by doobly
Tags: bernoulli, global, inhomogeneous, solution
 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.
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,460 As long as l(t) and v(t) are "Lipschitz" ("differentiable" is sufficient but not necessary) on [0, 1], that follows from the elementary "existance and uniqueness" theorem for intial value prolems of the for equations of the form y'= f(t, y).

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