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marvalos
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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 for t≥0. Show the solution of this IVP is bounded for t≥0. (Hint: Use the Variation of Constants Formula.)
Any help on where to go for this problem would be great. Thanks
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 for t≥0. Show the solution of this IVP is bounded for t≥0. (Hint: Use the Variation of Constants Formula.)
Any help on where to go for this problem would be great. Thanks