# Items tagged with differential_equationdifferential_equation Tagged Items Feed

### Solving an ode : Warning, it is required that the...

October 10 2014
1 3

Hello,

could you help me solve this error ? I don't understand what it means.

> eq3:=diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*(x(t)-(diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*x(t)+omega[0]^2*X[0])/omega[0]^2) = -omega[0]^2*X[0]:
> dsolve(eq3);
Warning, it is required that the numerator of the given ODE depends on the highest derivative. Returning NULL.

Thanks.

### Finding initial velocity of a ball...

October 10 2014
1 8

Dear all,

I am trying to find the intial velocity of a ball that is shot under an angle while only the start and end coordinates are given. The air resistance should also be taken into account.

In order to do that I have build the following Maple sheet:

I have used two differential equations that both include the variables v0 and t, and then try to solve them. Only I receive an answer in the form of RootOf, which I cannot remove with for example allvalues.

I have been working for quite a long time on this but I am not coming any further, so is there anyone who can find what I am doing wrong/what I should be doing else? Or maybe my whole approach is not right?

Even a small step in the right direction would be appreciated a lot!

Elise

### solution of wave equations...

September 23 2014
1 1

Please, how do i compute,solve and derive d' Alembert wave formula with maple since wave=How do i derive d'Alembert formula using maple and also how to solve any wave problems eg IC u(x,0)=1/2e^-x^2 and ut(x,0)-e^-x^2 when c=4

### How to solve this problem in Maple？...

August 01 2014
0 3

I want to get numerical solution of the Eqs.ode(see the folowlling ode and ibc）in Maple.However,when i run the following procedure,it prompts an error "Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution". How to solve the issue? Please help me.

restart:
n := 1.4; phi := 1; beta := .6931; psi := 1

> restart;
> n := 1.4; phi := 1; beta := .6931; psi := 1;

> s := proc (x) options operator, arrow; evalf(1+(phi*exp(beta*psi)*h(x))^n) end proc;

> Y := proc (x) options operator, arrow; evalf(f-(1/2-(1/2)/n)*ln(s(x))+2*ln(1-(1-s(x))^(-1+1/n))) end proc;

> ode := diff(h(x), $(x, 2))+(diff(Y(x), x))*(diff(h(x), x)+1) = 0; > ibc := h(0) = 0, ((D(h))(10)+1)*s(10)^(-(1-1/n)*(1/2))*(1-(1-1/s(10))^(1-1/n))^2 = 0; > p := dsolve({ibc, ode}, numeric); Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution > ### why the result of Differential equation solve is w... July 02 2014 1 3 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 ### nonlinear differential equation... June 08 2014 2 1 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 ### Solve Differential Equations... May 08 2014 2 3 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 ### Euler help please... April 23 2014 0 6 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 ### Second order direction field problems... March 29 2014 0 1 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. ### How to solve a differential equation on Maple? ... January 27 2014 1 17 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 with this differential equation, sin... December 16 2013 1 3 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 ### Error, invalid input: eval received params, which ... December 13 2013 1 3 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 ### what is X1 and X2 so that [X1, X2] = X1*X2 - X2*X1... December 07 2013 0 0 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;

### Plotting graphs and animations in Maple...

December 04 2013
1 6

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.

### Change of variables in differential equation...

December 03 2013
1 2

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.

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