Integro-differential equation

In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function. == General first order linear equations == The general first-order, linear (only with respect to the term involving derivative) integro-differential equation is of the form d d x u ( x ) + ∫ x 0 x f ( t , u ( t ) ) d t = g ( x , u ( x ) ) , u ( x 0 ) = u 0 , x 0 ≥ 0.