Items tagged with differential_equation

I wrote an equation and intended to iterate P(r) till that value of r when P(r) becomes 0.what is the value of r for which P(r)=0, and also  obtained its convergent decreasing graph which show convergence of P(r) to 0.



G := 6.6743*10^(-8);








sys2 := diff(P(r), r) = -G*(epsilon+P(r))*((8.98*10^14*(1/3))*Pi*r^3+4*Pi*r^3*P(r)/c^2)/(c^2*(r^2-(2*G*r*(8.98*10^14*(1/3))*Pi*(r^3))/c^2)), P(0.1e-9) = 8.5561*10^34

diff(P(r), r) = -0.7426160269e-28*(0.7321400000e36+P(r))*(0.2993333333e15*Pi*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.4445794614e-13*r^4*Pi), P(0.1e-9) = 0.8556100000e35






Hello! Hope everything fine with you. I am try to solve the three-point differential by numerical method in attached file but failed. Please see the attachement and solve my problem. I am very thankful your kind effort. Please take care.

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China





G := 6.6743*10^(-8); 1; c := 2.99792458*10^10; 1; pi := 3.143; 1; rho := 5.3808*10^14









diff(P(r), r) = -G*(rho*c^2+P(r))*((4*pi*r^3*(1/3))*rho+4*Pi*r^3*P(r)/c^2)/(c^2*(r^2-2*G*r*(4*pi*r^3*(1/3))*rho/c^2)), diff(v(r), r) = 1.485232054*10^(-28)*((4*pi*r^3*(1/3))*rho+4.450600224*10^(-21)*Pi*r^3*P(r))/(r^2-1.485232054*10^(-28)*r*(4*pi*r^3*(1/3))*rho)

diff(P(r), r) = -0.7426160269e-28*(0.4836021866e36+P(r))*(0.2254913920e16*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.3349070432e-12*r^4), diff(v(r), r) = 0.1485232054e-27*(0.2254913920e16*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.3349070432e-12*r^4)


condition; -1; P(0) = 0, v(1014030) = -.4283

P(0) = 0, v(1014030) = -.4283





I found the solution of P(r) at P(0)=0, but could obtain the result of v(r) at v(1014030)=-0.4283, v(r) may have a graph such that i can goes from -0.4283 to 0.

G := 6.6743*10^(-8);

a := 1.9501*10^24;

b := .3306;

c := 2.99792458*10^10;

d := 2.035;

pi := 3.143;

eps := 3.8220*10^35;

g(r) = 1-s(r)/0.06123;

j(r) = e^(-(1/2)*w(r))*(1-2*G*v(r)/(r*c^2))^.5

sys := diff(v(r), r) = 4*pi*r^2*eps/c^2, ics=v(0)=0

diff(u(r), r) = -G*(eps+u(r))*(v(r)+4*Pi*r^3*u(r)/c^2)/(c^2*(r^2-2*G*r*v(r)/c^2)),u(0)=1.3668*10^34

diff(w(r), r) = 1.485232054*10^(-28)*(v(r)+4.450600224*10^(-21)*pi*r^3*u(r))/(r^2-2*G*r*v(r)/c^2), conditions: w(0)=0,iterate it to find w(688240)=-2.05684, it solve must satistfy the both conditions.

diff(r^4*j(r)*(diff(g(r), r)), r)+4*r^3*g(r)*(diff(j(r), r)) = 0, conditions dg(r)/dr =0  at r=0, g(688240) =0.87214

diff(J(r), r) = (8*pi*(1/3))*(eps/c^2+u(r)/c^2)*(g(r)*j(r).(r^4))/(1-2*G*v(r)/(r*c^2)) condition J(0)=0.


dsolve({Q(0) = 0, Q(t) = (1.375*4190)*(80-T__1(t)), Q(t) = (1.375*4190)*(T__2(t)-38.2), diff(Q(t), t) = (0.1375e-1*(T__1(t)-T__1s(t)))*((T__1(t)+T__1s(t))*(1/2)), diff(Q(t), t) = (0.1375e-1*(T__2s(t)-T__2(t)))*((T__2s(t)+T__2(t))*(1/2)), diff(Q(t), t) = (240*0.1375e-1)*(T__1s(t)-T__2s(t))/(0.1e-2)}, numeric)

Error, (in dsolve/numeric/DAE/initial) missing initial conditions for the following: {T__1s}



i got 3 diff ecuations with two algebraic ones. a system of DAEs. there is only a derivative included on systems, for which it's necesary only one initial condition for solving the system, which is Q(0)=0. why maple wants to know initial conditions for T_1s. it's not supposed to calculate it itself?


I resolved the coefficients to a 2nd order diff eq of the form:ay''+by'+cy=f(t)

I have included the .mw file for convenience at the link at the bottom of the page.  I resolved the coefficients in 2 different ways & they do not concur.  The 1st approach used the LaPlace transform & partial fraction decomposition.  The coefficient results are given by equations # 14 & 15.  The 2nd approach used undetermined coefficients where I assumed the particular solution and then applied the initial conditions to resolve the coefficients pertaining to the homogeneous solution which are given in the results listed in equation #23.  Noted in the 1st case the coeff's are A3 & A4 and for the 2nd approach the coeff's are A1 & A2.  I have worked this numerous times & do not understand why they do not concur.  So I thought I should get some fresh eyes on the problem to find where I may have gone wrong.

Any new perspective will be greatly apprecieated.

I had trouble uploading the .mw file so I have included an alternative link to retrieve the file if the code contents is illegible or you cannot dowlad the file drectly from the weblink  Download  You should be able to download from the alternative link below once you paste the link into your browser.  If you cannot & wish for me to provide the file in some other fashion respond with some specific instructions & I will attempt to get the file to you.

Thanks 4 any help you can provide.


I am working on a maple lab assignment and we dont actually learn maple for the class we just use it do 5 assignment the whole semster. This one consists of damping and differential equations which we have not learned. I was wondering if anyone knew how to carry it out. Well here is the part where I have an issue: 

Our solutions in the critically damped and overdamped cases approach the θ = 0 axis without crossing it, but if the initial velocity is directed toward the equilibrium position and is sufficiently large the pendulum will “overshoot”, passing the equilibrium position before settling back toward it. Experiment with this effect with a new value µ = 8 of the damping constant to give overdamped motion: introduce a new initial condition (give it a new name), keeping θ(0) = 1 but changing θ '(0) until you find a value which produces an overshoot of about 0.1 radian. Include in the worksheet only the graph showing this overshoot and the commands needed to produce that graph. In the discussion section give explicitly the value of the initial velocity that you found.

And this was the original initial condition and equation code:

K:=9; deG:=diff(theta(t),t,t) + mu*diff(theta(t),t)+K*sin(theta(t))= 0; deL:=diff(theta(t),t,t) + mu*diff(theta(t),t)+K*theta(t)= 0; Iv:=theta(0)=1, D(theta)(0)=5; dom1:=t=0..10;

I am not too sure how to manipulte this to work. Any help is welcome. 

Please help me to solve the system of 1st order singular O.D.E  (see uploaded file)....New_Microsoft_Office_Word_Document.docx

sol_L := dsolve({de_L, ic});

    {x(t) = (-y0 - x0) exp(-2 t) + (y0 + 2 x0) exp(-t),
      y(t) = -2 (-y0 - x0) exp(-2 t) - (y0 + 2 x0) exp(-t)}
How i can plot this?thanks


Just thought I'd put a quick one in. I'm trying to solve the Schrodinger equation given as:

schro := {diff(psi(x), x, x)-((b^2-a*(2*p+3))*x^2+2*ab*x^4+a^2*x^6-energy)*psi(x) = 0};

under the constraint


I'm trying to plot this for a range of values of the parameters a,b and fixed p=0,1.

I'm aiming to get a solution of the form

psi(x)=(x^p) exp((-a(x^4))/4)-(b(x^2)/2)

and plotting it.

Thanks in advance

I am trying to solve in Maple the system 
d{x}/dt =(1  1 \\1  -1).{x}
with initial conditions {x(0)} =(1 \\ -1),
where {x} is a vector.

This is what I did up to now


but I am not sure how to correctly input the initial conditions to find a solution to the problem. I would appreciate any help provided.

i want to write the result of a calculation to a file in a way that i can be able to call them later. for example :

n := 40; h := 40;
a := h*i/(2*n);

sys1 := [diff(x(t), t) = 2*t+1, diff(y(t), t) = 1+5*t, x(0) = 1, y(1) = 0];

for i from 0 by .5 to 1 do res := dsolve(sys1, numeric); res(a) end do;

i would like to write just the values of t and y(t) to a file/vector or whatever.

Thx in advance

Hello all
I want to integrate an equation involving different terms (some of them involve derivatives) the following picture shows the expression and the end result. I can do it manually by multiplying both sides with u'. but how can acheive that in maple


Eq4 := diff(u(xi), xi, xi) = a[0]+a[1]*u(xi)+a[2]*u(xi)^2; Eq5 := int(Eq4, xi); simplify(%)

diff(diff(u(xi), xi), xi) = a[0]+a[1]*u(xi)+a[2]*u(xi)^2


Error, (in int) wrong number (or type) of arguments: wrong type of integrand passed to indefinite integration.


diff(diff(u(xi), xi), xi) = a[0]+a[1]*u(xi)+a[2]*u(xi)^2





I have tried to solve the following ode equation, but I have got error. What is the potencial problem?




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