## 1511 Reputation

8 years, 309 days

## Try this:N := 10;(MultiSeries:-series(si...

With package: MultiSeries Maple can:

N := 10;
(MultiSeries:-series(sin(x)^a, x = 0, N) assuming (0 < a));

#x^a - a*x^(2 + a)/6 + (-1/180*a + 1/72*a^2)*x^(4 + a) + (-1/2835*a + 1/1080*a^2 - 1/1296*a^3)*x^(6 + a) + (-1/37800*a + 101/1360800*a^2 - 1/12960*a^3 + 1/31104*a^4)*x^(8 + a) + O(x^(10 + a))

## Another simpler way to compute this...

Another simpler way to compute this integral:

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## A good question why inttrans does n...

A good question why inttrans does not work in this case? I don't know.

A trick:

inttrans:-fourier(- diff(erf(x), x)*I/k, x, k);

# -2*I*exp(-k^2/4)/k # A correct answer.

int(erf(x)*exp(-I*x*k),x=-infinity..infinity);

# -2*I*exp(-k^2/4)/k !

## evalf[10]...

evalf[10](Int(exp(-x)*sin(x^2/2)/(3 + x), x = 1 .. infinity));

#0.04279639331

Or:

Digits := 10:

int(exp(-x)*sin(x^2/2)/(3 + x), x = 1 .. infinity, numeric);

#0.04279639331

Execute: ?Digits ,to see more information.

## Try add assuming to integral....

with Maple 2019.2 :

int(1/(c*x + d), x = a .. b) assuming a < b;

#piecewise(And(a < -d/c, -d/c < b), undefined, (-ln(a*c + d) + ln(b*c + d))/c)

## closed form ?...

Do you have any reason to think there is a closed form? Most nonlinear ODE's don't have one.

With numerics,see attached file:

## BVP method only work....

You have a BVP type ODE ,RK methods dosen't work(in Maple) for yours ICS and BC.

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## Try this: >&nbs...

`After eliminating  syntax errors:`

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## Try this:...

Try this:

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## useint......

Command useint in dsolve helps:

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## Another workround:...

```simplify(int(sin(y)^(1/3)*cos(y)^3, y = 0 .. x, AllSolutions));

#piecewise(sin(x) < 0, FAIL, 0 <= sin(x), -3*(2*sin(x)^2 - 5)*sin(x)^(4/3)/20)```

## Pity......

Yes, Maple can't  handle elliptic PDEs,because last Updates(Enhanced) to solving PDE's equation was in Maple 9 in year 2003.

During this time  no improvements have been made.

What a pity.

## pdsolve can solve......

pdsolve can solve,on Maple 2019.1 with Physics:-Version(399):

PDE := diff(u(x, t), t) + 2*u(x, t)^2*diff(u(x, t), x) - diff(u(x, t), x)^2 - 1/2*diff(u(x, t), x \$ 2)*u(x, t) = 0;

pdsolve([PDE, u(x, 0) = -tanh(x)]);

#u(x, t) = tanh(t - x)

## Use simplify command:...

sol := solve({sin(9*x - 1/3*Pi) = sin(7*x - 1/3*Pi)}, [x], explicit, allsolutions);

seq(simplify(sol[j]), j = 1 .. nops(sol));

#[x = 2*Pi*_Z13], [x = Pi*(2*_Z14 + 1)], [x = -1/48*Pi + 2*Pi*_Z15], [x = 47/48*Pi + 2*Pi*_Z15], [x = #23/48*Pi + 2*Pi*_Z15], [x = #-25/48*Pi + 2*Pi*_Z15], [x = 5/48*Pi + 2*Pi*_Z15], [x = -43/48*Pi + #2*Pi*_Z15], [x = -19/48*Pi + 2*Pi*_Z15], [x = 29/48*Pi + 2*Pi*_Z15], #[x = -7/48*Pi + 2*Pi*_Z15], [x = #41/48*Pi + 2*Pi*_Z15], [x = 17/48*Pi + 2*Pi*_Z15], [x = -31/48*Pi + 2*Pi*_Z15], [x = 11/48*Pi + #2*Pi*_Z15], [x = -37/48*Pi + 2*Pi*_Z15], [x = -13/48*Pi + 2*Pi*_Z15], [x = 35/48*Pi + 2*Pi*_Z15]

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