## About numerical solution of DEs...

Hello friends!

I have one question, whenever I solved system of ODEs using numerical solution (bilton command i.e., dsolve(dsys1, numeric, output = listprocedure, range = 0 .. 1)), its accutacy always like 10 or 12 digits not above at all. I want to how i improve the accuracy. I am waiting your postive answer.

## Why Maple does not solve this simple system of dif...

Hi,

Can somebody help me to find out why Maple can't completely solve this system of differential equations?

The answer to the previous command is

but I don't get the solution for u(x). This should be u(x)=-x+x^2/2.

## Which method do maple use to dsolve differential e...

If algebra use factorise method,

Which method do maple use to dsolve differential equation?

## How do i fix the error"Newton iteration is not con...

Respected member!

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 > subject to boundary conditions
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## Newton iteration is not converging...

Respected member!

## Problem to solve differential equations and plot t...

Dear friends:

I am facing two problems

1. one is to get solution of the below system of ODE for L=100 (highlited as red) and

2. the other is I want the graph in the form of solid line not poit, asterisk etc.

restart; epsilon := .1; Pr := 1; beta := .1; Sc := 1; S := 1; L := 20;
for i from -L while i <= L do;
a[i] := 1.0*i/L;
end do;
for i2 from -L while i2 <= L do;

fw := a[i2];

Eq1[i2] := eval(diff(F(eta), eta, eta, eta)+F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2+S*(epsilon-(diff(F(eta), eta)))+epsilon^2);
Eq2[i2] := eval((diff(G(eta), eta, eta))/Pr-G(eta)*(diff(F(eta), eta))+F(eta)*(diff(G(eta), eta)));
Eq3[i2] := eval(diff(H(eta), eta, eta)+Sc*(F(eta)*(diff(H(eta), eta))-beta*H(eta)));
IC[i2] := F(0) = a[i2], (D(F))(0) = 1, (D(F))(L) = epsilon, G(0) = 1, G(L) = 0, H(0) = 1, H(L) = 0;
dsys1[i2] := {Eq1[i2], Eq2[i2], Eq3[i2], IC[i2]};
dsol1[i2] := dsolve(dsys1[i2], numeric, output = listprocedure, range = 0 .. L);
dsol1x[i2] := subs(dsol1[i2], diff(F(eta), eta, eta));
dsol1y[i2] := subs(dsol1[i2], G(eta));
dsol1z[i2] := subs(dsol1[i2], H(eta)) end do;

for j from -L while j <= L do;
g[j] := eval(-dsol1x[j](0)) end do;
with(plots);

g6 := pointplot({seq([n/L, g[n]], n = -L .. L)}, symbol = asterisk, symbolsize = 15, color = red);
display(g6);

Please see the problem and correct as soon as possible. I am waiting your positive respone.

School of Mathematical Sciences
Peking University, Beijing, China

## solve ode srm motor...

How I can solve it for P?

P=i^(2)r+(&DifferentialD;)/(&DifferentialD; t) (1/(2)l(tetha)i^(2))+1/(2)i^(2)(&DifferentialD;l(tetha))/(&DifferentialD; theta) w

attach i(t) "corrente", l(t) "induttanza", theta "angular", w "rotary speed"graph of funtions

thanks

## no output despite simple diffeq...

I get no output from the following

deqv := m*v(s)*(diff(v(s), s)) = m*g-k*v(s)^2

I have to write

solv := `assuming`([dsolve({deqv, v(0) = v__0}, v(s), implicit)], [v__0 > 0])

in order to get

-g*m/k-exp(-2*k*s/m)*(-g*m/k+v__0^2)+v(s)^2 = 0

and then I have to write my own function

It should be a piece of cake for maple to solve this!

Staffan

## Throwing a ball with aire resistance...

I'm trying to plot the velocity of a ball thrown upwards with air resistance proportional to v^2 and also some simpler forms of this.

But the solution to v^2 returns root of and the plot stops for some specific time value. How can I proceed this plot to let's say 10 sec?

Staffan

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## missing solution from dsolve? ...

I am not a math major, so may be I am missing something here. But for this ode:

(diff(y(x),x))^2=4 * y(x)

There ought to be (I think) 2 solutions (other than the singular one y(x)=0), due to the square root. i.e the ode becomes

diff(y(x),x)= +-  2* sqrt(y(x))

So for the + case, there is one solution, and for the - case, there is another solution. But Maple dsolve only gives one solution (again, ignoring the singular solution for now):

eq:=(diff(y(x),x))^2=4 * y(x);
sol:=dsolve(eq,y(x));

y(x) = _C1^2-2*_C1*x+x^2

In Mathematica, it gives both solutions

ode = (y'[x])^2 == 4 y[x];
DSolve[ode, y[x], x] // Simplify
{  {y[x] -> (1/4)*(-2*x + C[1])^2},   {y[x] -> (1/4)*(2*x + C[1])^2}}

Both Maple and Mathematica solutions are correct ofcourse. But my question is why did not Maple give both (non-singular) solutions? and it only gave one?

Maple 2016.2

## why this equation does not any answer?...

hi

why this equation does not any answer?

thanks

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 >
 > eq:={-J*g[1]*(diff(w(x), x, x, x, x, x, x))+J*c[1]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))+(beta[11]*A*0)*`ΔT`*(diff(w(x), x, x))+2*b*f[1133]*(Pi/L)^2*(d[33]*lambda[3]*`ΔT`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`ΔT`*L)*sin(Pi*x/L)*sinh(h*Pi/(2*L))/(2*cosh(h*Pi/(2*L))*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}
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## Trig simplification question, result from dsolve...

The ODE diff(y(x),x) = sec(x)^2*sec(y(x))^3  can be solved as separable. So the answer should be

as can be seen by direct integration of each side of the differential equation. I am trying to make Maple give the same answer, but not having any luck.

restart;
ode:=diff(y(x),x) = sec(x)^2*sec(y(x))^3;
sol:=dsolve(ode, y(x),implicit);

I tried simplify(sol,trig) and tried simplify(sol,size).  Both Maple answer, and the simple answer solve the ODE.

Is there a way to make Maple dsolve give the simpler answer, or simplify/convert the answer it gives to the simpler one? I am newbie in Maple.

## My system of equation was ODE, but Maple insists i...

I was trying to solve a system of ODE using Maple, but to my surprise, Maple recognizes diff((phi(t), t)) as a variable which is different than t.

My code is as following:

dsys := {2*m1*(a+l*sin(phi(t)))^2*(diff(diff(theta(t), t), t))+4*m1*(a+l*sin(phi(t)))*l*cos(phi(t))*(diff(theta(t), t))*(diff(phi(t), t)) = M, 2*m1*l^2*(diff(diff(phi(t), t), t))+4*m2*l^2*sin(2*phi(t))*(diff(phi(t), t))*(diff(phi(t), t))+4*m2*l^2*sin(phi(t))^2*(diff(diff(phi(t), t), t))-2*m1*(a+l*sin(phi(t)))*l*cos(phi(t))*(diff(theta(t), t))*(diff(theta(t), t))-2*m2*l^2*(sin(2*phi(t)))(diff(phi(t), t))*(diff(phi(t), t)) = -(2*(m1+m2))*g*l*sin(phi(t))-2*k*l^2*sin(2*phi(t)), phi(0) = 0, theta(0) = 0, (D(phi))(0) = 0, (D(theta))(0) = 0}

subs({M = 10, a = .5, g = 9.81, k = .1, l = .5, m1 = 10, m2 = 1}, dsys);

dsn1 := dsolve(dsys, numeric)

The error I got was Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, diff(phi(t), t)}

I don't get why this is happening. Could you show me what's going on?

## another division by zero using dsolve in Maple 201...

Hello; I found another ODE which Maple gives division by zero on.  Is this also a bug?

dsolve(x*(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)^2-(2*a^2*x*y(x)-(x^2-y(x)^2)^2)*diff(y(x),x)+a^2*y(x)^2-x*y(x)*(x^2-y(x)^2) = 0, y(x));

Error, (in dsolve) numeric exception: division by zero

This is from a book. Using Maple 2016.1 on windows.

## why Maple gives (numeric exception) from dsolve on...

Maple 2016.1 on windows. This ODE from a book, and Maple gives division by zero. Is this a bug or expected?

ode:=(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)+x*(x^2-y(x)^2) = a^2*y(x);
dsolve(ode, y(x));

Error, (in dsolve) numeric exception: division by zero

Mathematica gives this to same ODE, but no division by zero.

DSolve[x*(x^2 - y[x]^2) + (a^2*x + y[x]*(x^2 - y[x]^2))*y'[x] == a^2*y[x], y[x], x]

Solve[x^2/2 - (1/2)*a^2*Log[x - y[x]] + (1/2)*a^2*Log[x + y[x]] +y[x]^2/2 == C[1], y[x]]

Where is the division by zero coming from in Maple?

2016.1 on windows.

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