## 1436 Reputation

7 years, 357 days

## Correction....

Using assumption and infinity not Infinity, works fine.

Integrals_Sheet2-A.mw

## Using this package we can solve.Extract ...

One way is using this package.

Extract file aene_v1_0.tar to any folder then open a file Sample.mws and copy my code to the file and execute.

```eq:=diff(y(t),t\$mu)=0.85*sqrt(y(t)^2)-0.85*y(t)^2:
IC:=[y(0)=0.5]:
```

## Workaround....

Or workaround:

```restart;
T__ln := (1/2)*m__ws*v__l+(1/2)*I__ws*(diff(varphi__l(t), t))^2+((1/2*(m__zs+m__zp+m__wp))*v__l+(1/2*(I__zs+I__zp+I__wp))*(diff(varphi__l(t), t))^2)*z__11*eta/z__12+((1/2*(m__wk+m__zpk+m__k+m__zk))*v__l+(1/2*(I__wk+I__zpk+I__k+I__zk))*(diff(varphi__l(t), t))^2)*z__21*eta/z__22;
eval(diff(eval(T__ln, diff(varphi__l(t), t) = x), x), x = diff(varphi__l(t), t));
```

## 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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 > derivative
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## useint......

Command useint in dsolve helps:

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