Operator form of integro-differential equation

[sarrah1]

Hi

For brevity one usually writes Fredholm integral equation of the 2nd kind

$\psi(x)=f(x)+\int_{a}^{b} \,k(x,s)\psi(s) ds$

into the form

$\psi=f+K \psi$
where $K$ is the operator kernel

My question can one write an integro differential equation

$\d{\psi(x)}{x}=f(x)+\int_{a}^{b} \,k(x,s)\psi(s) ds$

into the form

${D}_{x}\psi=f+K \psi$

thanks

 

[Ackbach]

Yep. You just did!

 

[sarrah1]

Yep. You just did!

thank you indeed