## 1491 Reputation

8 years, 281 days

## ......

Calculating point with newton method:

```restart;
with(Student[NumericalAnalysis]):
with(plots):
f := x^3-x^2-x-1;
P := Newton(f, x = 2.0, tolerance = 10^(-2));
p1 := pointplot([[P, 0]], color = [blue], symbolsize = 20, symbol = circle, axes = normal):
p2 := plot(f, x = 0 .. 2.2):
display({p1, p2});
```

First iteration:

```evalf(eval(simplify(x-f/(diff(f, x))), x = 2));
# 1.857142857
```

## Answer for Legendre wavelets method for ...

Hi

I'm only changed "Equation" to "2*M" , "Solu" to "Solu[1]" and other things.

Regards Mariusz.

Help_v2.mw

## I'm not an expert on that topi...

I'm not an expert on that topic.

With help from: https://www.maplesoft.com/applications/view.aspx?sid=4971  (See: A Numeric Approach).

```restart;
f := proc (u) options operator, arrow; piecewise(0 <= u and u <= 1, 0, 1 < u and u <= 2, 1) end proc;
ode := diff(y(u), u\$2) = 4*Pi^2*(f(u)-e)*y(u); bc := y(0) = 0, y(2) = 0, (D(y))(0) = 1;
Eigen1 := (dsolve({bc, ode}, numeric, range = 0 .. 2, maxmesh = 8192, abserr = 1.*10^(-3), approxsoln = [y(u) = exp(-u), e = 1]))(0)[4];
Eigen2 := (dsolve({bc, ode}, numeric, range = 0 .. 2, maxmesh = 8192, abserr = 1.*10^(-3), approxsoln = [y(u) = u, e = 3]))(0)[4];
Eigen3 := (dsolve({bc, ode}, numeric, range = 0 .. 2, maxmesh = 8192, abserr = 1.*10^(-3), approxsoln = [y(u) = u, e = 6]))(0)[4];```

## textplot...

In Maple there is not much choice how to do it.

One of the possibilities is textplot.

```with(plots):
p1 := pointplot([[3, 8], [-5, 16], [11, 32], [3, -8]], color = [black], symbol = solidbox, axes = none, symbolsize = 12):
p2 := textplot({[-5, 16+2, "lampart"], [3, (-8)-2, "dog"], [3, 8+3, "cat"], [11, 32+4, "panthera"]}, axes = none):
p3 := implicitplot(y^2 = x^3-43*x+166, x = -40 .. 40, y = -40 .. 40, axes = normal, gridrefine = 2):
display({p1, p2, p3})
```

## Your formula is very complicated,closed...

Your formula is very complicated,closed form solution may be not exist(Mathematica also can't solve)

Maybe you can try a Numeric Inverse Laplace to solve your problem.

Help.mw

## Use initialvalue....

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Using another initalvalues:

```f := Fit(a*sin(b*x+c)+d, X, Y, x, initialvalues = [a = 50, b = 1/2, c = 1/2, d = 1120]);

#f := 48.7029442510649*sin(0.517394221899901*x+0.558920097492524)+1124.95011131587```

Maple gives almost the same as Geogebra

## Works fine,but where is the problem?...

Maple 2017.2 output:

```dsolve({B(t)*(diff(B(t), t, t))*A(t)-A(t)*(diff(B(t), t))^2-(diff(A(t), t, t))*B(t)^2+(diff(A(t), t))*B(t)*(diff(B(t), t))-A(t) = 0, diff(A(t), t) = 0});

#[{B(t) = B(t)}, {A(t) = 0}], [{A(t) = _C3}, {B(t) = (1/2)*_C1*(1/((exp(_C2/_C1))^2*(exp(t/_C1))^2)+1)*exp(_C2/_C1)*exp(t/_C1), B(t) = (1/2)*_C1*((exp(_C2/_C1))^2*(exp(t/_C1))^2+1)/(exp(_C2/_C1)*exp(t/_C1))}]```

## ......

```Digits := 20;
sol := 126*0.9 = int(14*t*exp(-(1/3)*t), t = 0 .. x);
solve({sol, x > 0}, {x})

#{x = 11.669160509602287174}
```

As procedure:

```UpperLimit := proc (percent) rhs(solve({(126/100)*percent = int(14*t*exp(-(1/3)*t), t = 0 .. x), 0 < x}, x)[1]) end proc;
UpperLimit(90)

#-3-3*LambertW(-1, -(1/10)*exp(-1))

evalf(UpperLimit(90))# 90%

# 11.669160509602287174

evalf(UpperLimit(50))# 50%

#5.0350409700499819602

evalf(UpperLimit(10))# 10%

#1.5954348251688360603```

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## Mathematica can solve....

Using SeriesCoefficient function:

## Weakness in convert...

Well, Maples convert(func,FPS) or convert(func,Sum) function is not strong enough.

Using Maxima http://maxima.sourceforge.net/  powerseries function:

tanh(x) = Sum((4^n-1)*4^n*bernoulli(2*n)*x^(2*n-1)/factorial(2*n), n = 0 .. infinity)

tanh(x+1) = Sum((4^n-1)*4^n*bernoulli(2*n)*(x+1)^(2*n-1)/factorial(2*n), n = 0 .. infinity)

Regards Mariusz

## Or symbolic solution....

restart;

k := 5;

EQ := diff(u(x, t), t) = k*(diff(u(x, t), x\$2));

ibc := u(0, t) = 0, u(1, t) = 0, u(x, 0) = x;

sol := pdsolve({EQ, ibc});

J := eval(subs(_Z1 = n, sol), infinity = 100);

int(value(eval(rhs(J), x = .5)), t = 0 .. 10)

(*0.01249999355*)

## Use 'explicit' :...

If You type:

sol := dsolve(diff(ln(y(x)), x) = y(x)^(1/(1-y(x))), y(x), 'implicit')

solution is implicit form.You must type:

sol := dsolve(diff(ln(y(x)), x) = y(x)^(1/(1-y(x))), y(x), 'explicit')

sol := y(x) = RootOf(x-Intat(_a^(-(-2+_a)/(-1+_a)), _a = _Z)+_C1)

form more details see:

`https://www.maplesoft.com/support/help/maple/view.aspx?path=dsolve%2fdetails`

but You can't solve this integral int(x^x,x) ,symbolic(analitically) solution does not exist yet,maybe in the future.

See this :

`https://en.wikipedia.org/wiki/Nonelementary_integral`

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## Try this...

```sol4 := fsolve([sol1, sol2], {T = 0...0.5, W = 0...30});

{T = 0.3216117634, W = 29.46435118}
```

Mathematica says the same what a Maple.

maple_solution.mw

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