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I'm trying to plot the direction field of the second order differential equation x''=x'-cos(x) using dfieldplot: 

> with(DEtools); with(plots);
> f1 := (x, y) options operator, arrow; diff(x(t), t)-cos(x(t)) end proc;
/ d \
(x, y) -> |--- x(t)| - cos(x(t))
\ dt /
> dfieldplot([diff(x(t), t) = y(t), diff(y(t), t) = f1(x(t), y(t))], [x(t), y(t)], t = -2 .. 2, x = -2 .. 2, y = -2 .. 2);
Error, (in DEtools/dfieldplot) cannot produce plot, non-autonomous DE(s) require initial conditions.
>

The error I'm getting says I need initial conditions, but I wasn't provided with any. Is there another way to plot this? Sorry if this is dumb question, but I've only ever plotted first order equations.

I have to solve a system composed of a mass, a spring and a damper, represented by this equation :

m (d2x/dt2) + c (dx/dt) + k x(t) = F(t)

with m the mass, t the time, c the constant of the damper, k the constant of the spring, F an external force applied to the mass and x(t) the movement of the mass m at time t.

Please help me to solve this equation on Maple.

What is wrong???

restart;
with(DEtools); with(plots);
epsilon := 'epsilon';

epsilon := 0.3e-1;
h := .75;
p := 2;
q := 0.6e-2;

sol := dsolve([[epsilon*(diff(x(t), t)) = x(t)+y(t)-q*x(t)^2-x(t)*y(t), diff(y(t), t) = h*z(t)-y(t)-x(t)*y(t), p*(diff(z(t), t)) = x(t)-z(t)], [x(0) = 100, y(0) = 1, z(0) = 10]], type = numeric);
%;
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

I write this system but I have 2 error

 

restart; params := [z = 0,

Omega = 2.2758,

tau = 13.8, T2 = 200,

omega0 = 1,

r = .7071,

s = 2.2758,

omega = .5]

 

sys1 := {diff(q(t), t) = -2*Omega*v(t)-s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*(y(t)-x(t))-q(t)/T2,

diff(v(t), t) = Omega*q(t)-v(t)/T2,

diff(x(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)+y(t)/T1,

diff(y(t), t) = -2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)-y(t)/T1};

ICs1 := {q(-20) = 0, v(-20) = 0, x(-20) = 1, y(-20) = 0}

 

 

ans1 := dsolve(`union`(eval(sys1, params), ICs1), numeric, output = listprocedure); plots:-odeplot(ans1, [[t, x(t)], [t, y(t)], [t, q(t)], [t, v(t)]], t = -20 .. 20, legend = [x, y, q, v])

 

Error, invalid input: eval received params, which is not valid for its 2nd argument, eqns
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

http://homepages.lboro.ac.uk/~makk/MathRev_Lie.pdf

ode1 := Diff(f(x),x$2)+2*Diff(f(x),x)+f(x);
with(DEtools):
with(PDETools):
gen1 := symgen(ode1);
with(PDEtools):
DepVars := ([f])(t);
NewVars := ([g])(r);
SymmetryTransformation(gen1, DepVars, NewVars);

Error, invalid input: too many and/or wrong type of arguments passed to PDEtools:-SymmetryTransformation; first unused argument is [_xi = -x, _eta = f*x]


generator1 := rhs(sym1[3][1])*Diff(g, x)+ rhs(sym1[3][2])*Diff(g, b)

what is X1 and X2 so that [X1, X2] = X1*X2 - X2*X1 = (X1(e2)-X2(e1))*Diff(g, z) ?

is it possible to use lie group to represent a differential equation, and convert this group back to differential equation ? how do it do?

 

how to find symmetry z + 2*t*a, when you do not know before taylor calcaulation?

fza := z + 2*t*a;
fza := x;
fza := z + subs(a=0, diff(fza,a))*a;

 

I am having some difficulty animating the function shown in the attached file.  I am going to create an animation which will show the curve as a function of t.  My first question is that there is no way to compute K_n because the initial conditions I have are only given as arbritary functions F(z),G(z).  So I am not really sure how to proceed here.

My second question is that I also want to plot the Z dependent part of y as a function of z/b.  I have tried to incorporate this into Maple, however, all I get back is that there are 'unexpected variables present'

Thanks.

Consider the differential equation zZ'' + Z' + a2Z = 0,  where Z = Z(z).  Using the change of variables x = \sqrt{z/b}with b a constant,  obtain the differential equation Z'' + (1/x)Z' + c2Z = 0, where Z = Z(x) and c = 2a \sqrt{b}.

I tried Maple help and it offers the dchange command, and what I have tried is shown below;

with(PDEtools):

DE:= ...

tr:= {z = x2b}

dchange(tr, DE)

This did not return anything however.  I am thinking I need to specify that b is a constant, however, I am a little unsure on how to do this. Is the above the correct way to proceed?  I don't see how I have specified anywhere that in the final PDE, I require Z=Z(x).

Thanks for any help.  This is my first post here, so apologies for the typesetting. If there is inbuilt latex, I will use it next time.

how to find lie group or finite group or symmetry group of one differential equation or system of differential equations

May I know how to use maple to solve

d^3y/dx^3+(1/x)(dy/dx)-(1/x^2)y=0, where y(1)=1, dy/dx=0 at x=1, d^2y/dx^2 =1 at x=1. find y(3).

 

Thx!

Solve the following initial value problem for y(t), z(t).

 

dy/dt + dz/dt =t

dy/dt-2 dz/dt=t^2

 

with initial condition y(0)=1, z(0)=2.

 

Thanks.

 

any general method to eliminate the derivative of lambda1,lambda2,lambda3

a:= -(diff(lambda1(t), t))+lambda3(t);
b:= -lambda1(t)-(diff(lambda2(t), t))+4*lambda3(t);
c:= -lambda2(t)+3*lambda3(t)-(diff(lambda3(t), t));

result in 2*lambda1(t) - lambda2(t) + 2*lambda3(t) = 0;

f := Diff(u(t),t$2)+Diff(u(t),t)+u(t)+x(t);

 

after indicate to extract u(t), should output Diff(u(t),t$2)+Diff(u(t),t)+u(t)

after indicate to extract x(t), should output x(t)

I am a student taking differential equations and I need to implement Euler's method using Maple 17. I have set up a do loop that looks like this:

for i from 1 to n1 do
k:= f(t,v):
v:= v + h*k:
t := t + h:
od:

Where n1 is initialized to 50, f(t,v) := 0.0207v2 -893.58, and h is 0.1. v and t are both initialized as 0.

How to find the exact solution from this equations?

1. (x+epsilon*y)dy/dx + y =0      y(1)=1

2. (x^n + epsilon * y)dy/dx + nx^(n-1) * y = m*x^(m-1)      y(1)=b>1   ; n=2,3,4,...   ; m=0,1,2,3,...

3. u" + u + epsilon*u^3 = 0    u(0)=A  ;   u'(0)=0

4. y" + 2(y')^2 +3y' = -sin x    ; y(0)=1  ;  y'(0)=0

 

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