Why is it that maple produces an incorrect answer in this command:

`assuming`([RealDomain[solve](sec(x) = sqrt(2), {x}, useassumptions)], [x > 3*Pi*(1/2) and x < 2*Pi])

and no answers in this command:

RealDomain[solve]({x > 3*Pi*(1/2), sec(x) = sqrt(2), x < 2*Pi}, {x})

???  Please help???

I was attempting to construct  a log question and noticed a problem with the answers that are being resolved by maple.

restart:
with(StringTools):
a := 2:
b := 10:
 c := -4:
d := 5:
rs := 4:
#notice I use the word filler below, in order to randomize later and replace "filler" with various "log[base]" or "ln".
equation1 := convert(filler(a*x+b)-filler(c*x+d) = rs, string):
equationAct := parse(SubstituteAll(equation1, filler, cat(ln))):
answer := [solve(equationAct, x)]:

#it appears maple is applying the log properties and suggesting solutions outside the real domain, for the individual log expressions.  The plot of the equation seems to confirm this.
plotA := plot(lhs(equationAct), x = -10 .. 10):
plotB := plot(rhs(equationAct), x = -10 .. 10):
plots[display](plotA, plotB);

Please help...

answer := 5*exp(7.5*t);

response := subs(a = exp(1), 5*a^(7.5*t));

a := evalf(subs(t = Pi, answer));

b := evalf(subs(t = Pi, response));

evalf(a-b);

Any explanations as to why the last line is not zero?  any workarounds?

I would like to perform an implicit differentiation of the following:

eqn := 5*(x*y)^2+x/sqrt(y) = x^2+2*(3*x^3+y^2)^3

However implicitdiff(eqn, x, y); produces an output that expands the result.  Is there a way to not have it expand?

I tried something to the effect of...

eqn := 5*(x*y(x))^2+x/sqrt(y(x)) = x^2+2*(3*x^3+y(x)^2)^3;

diff(eqn, x);

but now what I need to to isolate d/dx y(x)...

Any suggestions are much appreciated.

I am attempting to have maple recognize the difference in singularities between:

f(x)=x+1  and

g(x)=(x+1)*(x-2)/(x-2)

In other words how can I stop maple from simplifying g(x) and observe the singularity.

Thanks in advance.

Mark