4 years, 67 days

## Solve inverse trig equation...

Maple 2018

Hello,

I'm trying to solve  inverse trigonometric equation:

EQ := sqrt(3)*arctan(x/sqrt(3))-arctan(x) = 1;

sol := solve(EQ, {x});

#sol := {x = sqrt(3)*tan(RootOf(-tan(sqrt(3)*_Z-1)*sqrt(3)+3*tan(_Z)))}

evalf(sol);

#{x = 13.24164497} OK. one Real solution.

sol2 := evalf(allvalues(sol));

#sol2 := {x = -.1141310781-1.108044977*I}, {x = -.1141310781+1.108044977*I}, # {x = 1.142681884}, {x #= -2.379974990}, {x = 13.24164497}

Check:

seq(evalf(eval(EQ, sol2[k])), k = 1 .. nops([sol2]));

#.99999999991340592650+1.61960960*10^(-11)*I = 1., .99999999991340592650-#1.61960960*10^(-11)*I = 1., .15821278548775934290 = 1., -.4580182246463005988 = 1., #.9999999996233630663 = 1.

1.Can someone explain to me where did Maple find these Additional roots like: {x = 1.142681884}, {x = -2.379974990}?

2.It's a Bug or normal behavior ?

## Integration in a region?...

Maple 2018

I want to calculate and reproduce this question  in Maple.

with(Optimization):

f := (x, y) -> op(1, NLPSolve(sin(a*x*y), a = 1 .. 5));

int(`if`(f(x, y) > 0, 1, 0), [x = 0 .. 1, y = 0 .. 1], numeric);

# 0

,but I FAIL.

It should give me: 0.922105

Thanks.

## Differentiation and Integration with Int...

Maple 2018

In Maple 2018 help written:

The interpolation methods available in the Interpolation package all work as follows. First, the user calls one of the commands in the package, submitting the input points and the values at these points. This returns an object encapsulating all the data and options submitted. This object can then be used like a normal mathematical function, e.g. for plotting, integration, or just to evaluate at a given point.

The Interpolation[Interpolate] command was introduced in Maple 2018

My test example:

with(Interpolation):

points := [seq(x, x = 0 .. 10, 1)]; data := [seq(sqrt(1.+x^2), x = 0 .. 10, 1)];

f := Interpolate(points, data);

f(1); # OK works :).

int(f(x), x = 0 .. 1); # Not working ?

int(f(x), x = 0 .. 1,numeric); # Not working ?

eval(diff(f(x), x), x = 2);# Not working ?

plot(f(x), x = 0 .. 10);#  OK works :)

plot([f(x), diff(f(x), x)], x = 0 .. 10);# Not working ?

plot([f, diff(f, x)], 0 .. 10);# Only a half  working ?

Thanks.

## pdsolve: PDE by series?...

Maple 2018

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

It's a bug, design or  something else ?

## Calculate integral?...

Maple 2018

int(exp(-sec(t))*cos(t)/(-1/4+sin(t)^2), t = 0 .. (1/2)*Pi, CauchyPrincipalValue = true, numeric = true);

Returns unevaluated for me.

```I tried all the methods in HELP documentation and I failed.
Integral is singular at point 1/4.

```

Thank you.

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