I am stuck on the problem:
Find all continuous functions $h$ satisfying $\int_{0}^{x}h(y)dy=\left [ h(x) \right ]^{2}+C$ for some constant $C$.
I am stuck on the problem:
Find all continuous functions $h$ satisfying $\int_{0}^{x}h(y)dy=\left [ h(x) \right ]^{2}+C$ for some constant $C$.
HINT: The left hand side is known to be differentiable by the fundamental theorem of calculus, so the right hand side is also differentiable. Differentiate both sides to form a differential equation, and then solve that.