# Questions tagged [integro-differential-equations]

An integro-differential equation is an equation involving both the integrals and derivatives of a function. The solution to an integro-differential equation is a function which satisfies the original equation.

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### Advection-style first order nonlinear PDE system

Given functions $a(t,x,y) > 0, d(t,x) >0$ and constants $b,c > 0$, I would like to find the three functions $u(t,x),v(t,x) , w(t,x,y)$ that solve the system: \begin{align} u_t - u_x &= -\...
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### How to solve non linear integro-differential equation

I am trying to find a solution for this equation: $$f(t)-kt+\int_0^tg(t-\tau)\frac{df^2}{d\tau}d\tau=0$$ I know the $g(t)$ function and I have initial conditions $f(0)$ and $f'(0)$, but I really don't ...
Does this linear integral equation defined on $[-a,a]$ have any nonconstant solution? I am more interested in the exsistence of solution rather than the solution itself. The boundary condition has two ...