Recent content by marvalos

Here is what I have tried: The Variation of Constants formula gave me this x=(x0+∫e^u q(u) du) e^-t the integral is definite and goes from 0 to t. Since q(t) is bounded, would that remain true if the integral is taken from it?

The Variation of Constants formula is a generalized formula for First Order Linear DE's that can be solved with the Integrating Factor Method. I would put the exact formula down but I am not too familiar with this equation editor.

Proof on Linear 1st Order IVP solution being "bounded" A function h(t) is called "bounded" for t≥t0 if there is a constant M>0 such that |h(t)|≤M for all t≥0 The constant M is called a bound for h(t). Consider the IVP x'=-x+q(t), x(0)=x0 where the nonhomogeneous term q(t) is bounded...