Non-linear differential equation existence and uniqueness of solution

Question

I am very unfamiliar with the theory of nonlinear differential equations. Is there any result that given some initial conditions ensure the existence and uniqueness of a solution to the following: $af(x)=c-bf'(x)^2+f'(x)(tx+e)+kf''(x)$ for all $x,a,b,c,t,e,k\in \mathbb{R}$.