A differential equation involves functions and derivatives.
Integral equations involve functions and integrals.

In this example you have an integral equation. First you have to differentiate both sides. Then you have to solve a differential equation where you should be able to spot the solution immediately. Then you have to check that you have found a solution by substituting the function you have found into the integral equation.

In this example you have an integral equation. First you have to differentiate both sides. Then you have to solve a differential equation where you should be able to spot the solution immediately. Then you have to check that you have found a solution by substituting the function you have found into the integral equation.