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solve Differential equation "a-y=y' bc" use maple 17

the result is y(x)=a+_C1e^-(1/bc)

but the correct result  isn't y(x)=a-_C1e^-(1/bc) ?

Thank you in advance for your help

 

please help me to find an analytical approach to the below equation:

> ode3 := diff(n(t), t)+(1/2)*(-(3.707186000*(0.815e-1*(diff(n(t), t, t))+diff(n(t), t)))/(0.815e-1*(diff(n(t), t))+n(t))^(3/2)-(.1428*(1+0.714e-1*n(t)))*(diff(n(t), t)))/sqrt(7.414372/sqrt(0.815e-1*(diff(n(t), t))+n(t))-(1+0.714e-1*n(t))^2)+n(t)+sqrt(7.414372/sqrt(0.815e-1*(diff(n(t), t))+n(t))-(1+0.714e-1*n(t))^2)-(2.518891688*(1+.3570*n(t)))*sqrt(0.815e-1*(diff(n(t), t))+n(t)) = 0;
                                                                           /
                                                                           |
/ d      \                                 1                               |
|--- n(t)| + ------------------------------------------------------------- |
\ dt     /                                                           (1/2) |
               /           7.414372                                2\      |
             2 |------------------------------- - (1 + 0.0714 n(t)) |      |
               |                          (1/2)                     |      \
               |/       / d      \       \                          |       
               ||0.0815 |--- n(t)| + n(t)|                          |       
               \\       \ dt     /       /                          /       
              /       / d  / d      \\   / d      \\
  3.707186000 |0.0815 |--- |--- n(t)|| + |--- n(t)||
              \       \ dt \ dt     //   \ dt     //
- --------------------------------------------------
                                     (3/2)          
           /       / d      \       \               
           |0.0815 |--- n(t)| + n(t)|               
           \       \ dt     /       /               

                                        \       
                                        |       
                              / d      \|       
   - 0.1428 (1 + 0.0714 n(t)) |--- n(t)|| + n(t)
                              \ dt     /|       
                                        |       
                                        |       
                                        /       

                                                           (1/2)
     /           7.414372                                2\     
   + |------------------------------- - (1 + 0.0714 n(t)) |     
     |                          (1/2)                     |     
     |/       / d      \       \                          |     
     ||0.0815 |--- n(t)| + n(t)|                          |     
     \\       \ dt     /       /                          /     

                                                             (1/2)    
                                   /       / d      \       \         
   - 2.518891688 (1 + 0.3570 n(t)) |0.0815 |--- n(t)| + n(t)|      = 0
                                   \       \ dt     /       /         
> ics := n(0) = 0, (D(n))(0) = 674.5142595;


thanks and regards

louiza

 

AOA... Dears! When i solve the following differential equations

-(diff(lambda(s), s))-2*(diff(lambda(s), s, s))-(diff(lambda(s), s, s, s)) = 0

i got

lambda(s) = _C1+_C2*exp(-s)+_C3*exp(-s)*s

 here _C1,_C2 and _C3 are constant of intergration but i want the constant of integration of the following type

C[1],C[2] and C[3]

due to some reson pl help

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
  local no_points,x_old,x_new,y_old,y_new,i:
  no_points:=round(evalf((xn-x0)/h)):
  x_old:=x0:
  y_old:=y0:
 
  for i from 1 to no_points do
      x_new:=x_old+h:
      y_new:=y_old+evalf(h*f(x_old,y_old)):
      x_old:=x_new:
      y_old:=y_new:
  od:
  y_new:
end:


Thanks

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;

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