Let's start off slow, with some basic syntax.

Did you intend
   sin(x)
where you had entered (in 2D Math mode)
   sin x
?

@Axel Vogt Nicely done.

@pik1432 The other answers all used your additional helper equation eq_Dx, whereas the answer I gave did not need it. (I was supposing that you might have created that additonal equation manually.)

But, given your additional eq_Dx, then your target can be obtained by,

@mmcdara You're a little close (IMO) to suggesting that it is the imaginary unit I in particular that is the cause of your difficulty, and that would not be accurate.

In fact similar difficulties exist for compound products involving several extra multiplicands in the coefficient, even without I being present.

As sursumCorda has explained, it is due to the fact that your target term is not structurally present in the rhs.

Consider the example below. The term c*Int(f(x),x), ie. the lhs(eq), is not structurally present in rhs(eq). That is the case, even though the printing gives that appearance.

The "sub-product" c*Int(f(x),x) is not an actual structural component of the product 2*b*c*Int(f(x),x).

@tomleslie I asked whether he wanted just some kind of reflection (for which I too would have reflected/other, and spoofed the tickmarks, etc).

But the OP wrote, "However, I will like the horizontal axis to remain 0 to 15 but on the vertical axis, instead of having it going from 1 down to zero, I want it to be from 1 going up to 2."

What do you imagine that is supposed to mean?

I can concoct several different kinds of mapping that do that to an arbitrary curve, but it's unclear whether any of them are what's wanted. The goal is -- as yet -- not adequately specified.

@jmakinde The vertical position of the curve, at any horizontal value 't', is a consequence of the mathematical nature of the function. It's a math aspect, not a Maple aspect.

Suppose I plot A=t^2 between t=0 and t=3. It ascends from A=0 to A=9. How should I respond to the request that instead it descends from A=18 down to A=9?

@jmakinde I don't understand what you're saying, sorry.

Do you want to change the values of the curve?

Can you not provide some other curve/function, and show an analogous (but unambiguous) result with a similar kind of mapping?

@jmakinde I don't really understand what you mean, sorry.

I'll note that you have not provided your actual ODE. Is there a reason for that?

Are you trying to say that you want the values reversed on the x-axis, ie. going from say 15 to zero and one moves from left to right?

@jmakinde For asterisk or cross you would use style=point (instead of linestyle=dot and the default style=line).

For example,

plots:-display(
  plots:-textplot([4.4,120,N(t)]),
  plots:-odeplot( sol7, [t, N(t), color = red,
                  style=point, symbol=asterisk, symbolsize=12],
                  0 .. 5, numpoints=30),
  labels = [t,N(t)], size=[475,400] );

The file has not been attached.

Do you want to shade or color the basin of attraction of a univariate equation when using Newton's method? Would that be as a function of the complex-valued starting point?

If so, do you want it shaded/colored according to which root it converges to (eg. here), or according to how many iterations it takes to converge (eg. here).

What is an example of your kind of equation? Does your equation contain special-function calls, or calls to non-evalhf'able procedures? Or, perhaps, it just involves rational polynomials, or...?

@ijuptilk The ways that were suggested apply the substituion process to all of the expression or to all of the coefficients of derivatives (possibly simplified). And, in a way, the offered solutions are concocted to "get lucky", in the sense that the subexpression for replacement doesn't occur anywhere else, but only as the coefficient of your chosen derivative.

For example, I'm guessing that you would not want this accidental result:

In general such an coincidental, unwanted substitution could also occur when using plain subs, if the target coeffcient also appeared elsewhere in the expression.

It seems that the spirit of your question may be to only substitute for the coefficient of your chosen derivative. So, straightforward and possibly more robust (in general) in the sense just mentioned,

@Carl Love Sorry, you're quite right. I had already tried simplify-with-side-relations, getting the same result as you. Hence I was expecting to see it in Tom's answer, and somehow misread his call.

@Carl Love Does that produce a result for you which is different from what Tom showed with his second approach, ie. simplify with side relations, without a third argument?

Please put your followup queries for this problem here, instead of spawning completely separate new Question threads on it.