# Differential equation problems

1. Dec 2, 2005

### eljose

let be the differential equation in the form...

$$L[y]=a_{0}y+a_{1}y´+a_{2}y´´-f(x)=0$$

then you could use your theory of differential equation to solve and get the solution y=y(x), my first question is if knowing the value of y1=Y(x) and y2=g(x) being y1 and y2 solutions of the differential equation, could we obtain the values of $$a_{0},a_{2},a_{1}$$ i think you could use the Wronskian W(x) and the solution to this come from setting W(x)=0 adn from this you get the values of the a,s..

the other question is given the differential operator..

$$L[G(x,s)]=\delta(x-s)$$ with G(x-s) known how could obtain the a,s? (this is the inverse to the Green operator theory)..

and the last question...given the differential operator..

$$L[y]=a_{0}+a_{1}D^{1}+a_{2}D^{2}=0$$

where the functions a,s are function of x a=A(x) for every a then how could you obtain the adjoint operator?..thanks.