I am playing around with the symbolic engine in Mathcad Prime 2. Although my need is trivial (and can be done by visual inspection) despite this I cannot find a way to instruct Mathcad to do it. What I need is a way to insert an infinitesimal difference operator into an equation and multiply it by the differential operator. I accept that I may have overlooked something that others may find obvious but nevertheless I cannot achieve it. What I want to do is to multiply each side of the the following equation by "dt" and then integrate each side to find the function. The integration part is also trivial but the multiplication part escapes me. If there is an obvious work-around pray tell.
This is the example need:
Unless my algebra is incorrect, I agree that if one multiplies by dt on the left you get K*dt but on the right of the equation the integration variable should be dF(t) and not dt. If that so? However, Mathcad will not accept this. The only alternative that I see is substituting F for F(t) and performing the integration but I believe that is not equivalent. But why can I not get Mathcad to do the algebra for me? How can I multiply by dt on both sides of the equation using the symbolic engine.?
You mean like this:
Mathcad treats d/dt as a single operator, not as d(something) divided by dt, so to integrate anything you need to use the integration operator. Mathcad doesn't understand dt on its own.
I think you have found out the awful truth yourself.
In contrary to other math software, Mathcad provides no way to manipulate equations other than to solve them for a specific variable. No way to access LHS or RHS via a command, no way to add an expression on both sides or multiply the equation with an expression (disreagrading that, while quite common, its not entirely unproblematic to multiply by a differential operator.)
The same applies to your try to change an integration variable for a function F(t). Mathematically not unproblamatic, too, Mathcad simply refuses to do so, Prime won't let you type it in.
The necessary substitution, you mentioned, can be done with Mathcad, but would require an additional step/variable - quite awkward.
In Mathcad 15 there are the same restrictions. Only the (re)substitution can be done in one step.