What does "solution x" mean? What is "x" here?
Hi all,
I'd be very happy if you could help me solve a problem in my research.
I need to prove the following:
k is a constant.
y is strictly increasing, but not continuous.
Let .
denotes solution x.
.
for all .
for all .
Show:
for all .
The solutions of a differential equation obviously must be "differentiable" so must be continuous. So if for some and for some , there must exist between and such that .
But by the "existence and uniqueness" theorem, since there can be only one solution to this first order differential equation having a given value at .