## 1436 Reputation

7 years, 357 days

## Try: simplify(pdetest(sol, sys)); giv...

Try:

`simplify(pdetest(sol, sys));`

gives:

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

## General formula for n...

Maybe this helps, see attached file:

General_formula_.mw

## Or try:...

```simplify(diff(int(JacobiSN(x, k)^2, x), x));
```

#JacobiSN(x, k)^2

See attached file:

EQ_v3.mw

## Only......

Only solution,not  phase portrait.See atached file.

Solution.mw

## A way:...

One way is:

`[seq(rhs(op(1, rootsq0[[n]])), n = 1 .. numelems([rootsq0]))];`

## Maybe...

Maybe like this:

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/integrals.mw .

## Symbolic solution....

I don't have Maple 18.I don't understand what you mean by: h^k (0)=0 for k=0..n  ?

Solution by LaplaceTransform:

See attached file:

frac_eq_2.mw

## odetest...

```sol := dsolve((D@@2)(z)(t) + 2*D(z)(t) + z(t) = 2*exp(-t));
odetest(sol, (D@@2)(z)(t) + 2*D(z)(t) + z(t) = 2*exp(-t));
#0 ok.
```

```odetest(z(t) = t^2 + exp(-t), (D@@2)(z)(t) + 2*D(z)(t) + z(t) = 2*exp(-t));
#2 - 2*exp(-t) + 4*t + t^2```

is not true.

## Another way:...

```genfunc:-rgf_pfrac(1/(z^2 + I)^2, z);

#(-1/4 + I/4)*sqrt(2)/(-sqrt(2)*I + sqrt(2) + 2*z) + I/(-sqrt(2)*I + sqrt(2) + 2*z)^2 + I/(sqrt(2)*I - sqrt(2) + 2*z)^2 + (1/4 - I/4)*sqrt(2)/(sqrt(2)*I - sqrt(2) + 2*z)```

## plot...

Using LaplaceTransform and Inverse LaplaceTransform. Fractional derivative is Riemann–Liouville sense.

```restart;
v := t -> t;
plot([seq((inttrans:-invlaplace(s^alpha*inttrans:-laplace(v(t), t, s), s, t) assuming (0 < t)), alpha = -1 .. 1.5, 0.5)], t = 0 .. 10, view = [0 .. 9.5, 0 .. 5], legend = [seq('alpha' = alpha, alpha = -1 .. 1.5, 0.5)], color = [red, blue, green, yellow, cyan, magenta], axis[2] = [gridlines = [linestyle = dot]]);```

Elzaki transform by Laplace Transform, see attached file.

Elziki_transforms_vs_2.mw

## Maybe......

Maybe:

```func1 := h(x) = 2/f(x);
func2 := diff(func1, x);
subs([diff(h(x), x) = D(h)(-1), diff(f(x), x) = 2, f(x) = 4], func2);```

#h'(-1) = -1/4

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