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'Weekly Challenge 29: Integral Equation' printed from http://nrich.maths.org/
Find the function $f(x)$ which solves the equation $$\int_0^x
f(t)\,dt = 3f(x)+k\,,$$ where $k$ is a constant.
know ... ?
In the same way that a differential equation is formed from
differentials, an integral equation is formed from integrals.
Problems in mathematics might naturally be specified in terms of
integrals, others in terms of differentials. Differentials are
mainly used when the problem involves only local changes, such as
the force at a point, whereas integrals are used where the problem
involves a global property of a system, such as the total