Hello,

Here is the code I used to generate the image:

densityplot(x,x=0..1,y=-0..0.1,colorstyle=HUE,style=patchnogrid,scaling=constrained,view=[0..1,0..0.1],axes=none);

Then, I exported the image in a eps format. When the file is displayed, white lines appear as a grid. The problem comes from Maple and not from the softwares used to visualize the image. I tried so many things to solve that but...

How to solve the problem?

Thank you.

Jaqr

how to change the ode polt color for the below code

with(plots); 

R1 := .1; R0 := .1; m := .1; a := .1; Ha := .1; Nt := .1; Nb := .1; Pr := 6.2; Le := .6; Bi := 1; Ec := .1; k := 1; r := .1; A := 1; 

fcns := {C(y), T(y), U(y), W(y)};

 sys := diff(U(y), `$`(y, 2))+(R1*(diff(U(y), y))-2*R0*W(y))*exp(a*T(y))-a*(diff(U(y), y))*(diff(T(y), y))-Ha = 0, diff(W(y), `$`(y, 2))+(R1*(diff(W(y), y))+2*R0*U(y))*exp(a*T(y))-a*(diff(W(y), y))*(diff(T(y), y))-Ha = 0, diff(T(y), `$`(y, 2))+R1*Pr*(diff(T(y), y))+Pr*Ec*exp(-a*T(y))*((diff(U(y), y))*(diff(U(y), y))+(diff(W(y), y))*(diff(W(y), y)))+Pr*Ha*Ec = 0, diff(C(y), `$`(y, 2))+Pr*Le*R1*(diff(C(y), y))+Nt*(diff(C(y), `$`(y, 2)))/Nb = 0;

bc := U(0) = 0, W(0) = 0, C(0) = 0, (D(T))(0) = Bi*(T(0)-1), U(1) = 0, W(1) = 0, C(1) = 1, T(1) = 0; 

L := [.5, 1.0, 1.5, 2.0]; AP := NULL; 

for k to 4 do R := dsolve(eval({bc, sys}, Ha = L[k]), fcns, type = numeric, AP); AP := approxsoln = R; p1u[k] := odeplot(R, [y, U(y)], 0 .. 1, numpoints = 100, labels = ["y", "U"], style = line, color = ["black", "blue", "red", "pink"]) end do; 

display({p1u[1], p1u[2], p1u[3], p1u[4]})

I have a multiple integration. I know my integrals exist. When I write procedure for Rimannian sum, Maple gives correct answers for every choice of parameters of my integral. But when I ask Maple to compute it with int(...,numeric) sometimes it shows a correct answer and sometimes it shows a wrong answer. I'm curios to know what is going wrong in Maple, is there any command to see the details and steps of the computation to see where Maple is going wrong? I also increased the number of digits after decimal from 10 to 12 and 14. But Maple just repeats the wrong answers with just two or four digits. So the problem is not related to the approximation arising from number of decimals.

I was calculating the total derivative of a function but maple does not respond to the commands like alias,diff,totaldiff etc.

please see the attached pdf.multiplier.pdfmultiplier.pdf

fsolve does not any answer!!!!

please help me.

fsolve.mw

Dear users!

Hope everyone should be fine here. I need the following simiplification. I did it step by step is there and maple command to do this.

I am waiting your positive answer.

(diff(theta(eta), eta, eta))*(Rd*T[infinity]^3*(`θw`-1)^3*theta(eta)^3+3*Rd*T[infinity]^3*(`θw`-1)^2*theta(eta)^2+(3*(Rd*T[infinity]^3+(1/3)*epsilon*k[nf]))*(`θw`-1)*theta(eta)+Rd*T[infinity]^3+k[nf]) = (-3*Rd*T[infinity]^3*(`θw`-1)^3*theta(eta)^2-6*Rd*T[infinity]^3*(`θw`-1)^2*theta(eta)+(-3*Rd*T[infinity]^3-epsilon*k[nf])*(`θw`-1))*(diff(theta(eta), eta))^2+(-(rho*c[p])[nf]*nu[f]*f(eta)-(rho*c[p])[nf]*nu[f]*g(eta))*(diff(theta(eta), eta))+a*nu[f]*mu[nf]*(diff(f(eta), eta))^2/((-`θw`+1)*T[infinity])-2*a*nu[f]*mu[nf]*(diff(g(eta), eta))*(diff(f(eta), eta))/((`θw`-1)*T[infinity])+a*nu[f]*mu[nf]*(diff(g(eta), eta))^2/((-`θw`+1)*T[infinity])

(diff(theta(eta), eta, eta))*Rd*T[infinity]^3*(theta(eta)*`θw`-theta(eta)+1)^3+(diff(theta(eta), eta, eta))*k[nf]*(epsilon*theta(eta)*`θw`-epsilon*theta(eta)+1)+3*Rd*T[infinity]^3*(`θw`-1)*(theta(eta)*`θw`-theta(eta)+1)^2*(diff(theta(eta), eta))^2+epsilon*k[nf]*(`θw`-1)*(diff(theta(eta), eta))^2

diff((theta(eta)*`θw`-theta(eta)+1)^3*(diff(theta(eta), eta))*Rd*T[infinity]^3, eta)+diff((epsilon*theta(eta)*`θw`-epsilon*theta(eta)+1)*(diff(theta(eta), eta))*k[nf], eta);

Dear friends,

maybe, somebody knows how to remove annoying text of the first line of a Code Edit Region when a Region is collapsed.

Here, Region in expanded state:

But after collapsing the first line still remains:

i want to prove that :int(2*(sin(theta)/cos(theta))^2*p-1,theta=0..Pi/2)=Pi/sin(p*Pi), can anyone help me ?

when I  have transformed symbol expression  from matlab 2017b to  maple 2018 , maple took a mistake that  "maple kernel connection not available", What  is the  reason？Can anyone help me？Thank you！

Untitled2.pdf

Calculate S (100) by constructing a procedure "CalculesS" based on two iterative loops for, as

sys[1] := [-(diff(u(x, t), t, t))-(diff(u(x, t), x, x))+u(x, t) = 2*exp(-t)*(x-(1/2)*x^2+(1/2)*t-1), u(x, 0) = x^2-2*x, u(x, 1) = u(x, 1/2)+((1/2)*x^2-x)*exp(-1)-((3/4)*x^2-(3/2)*x)*exp(-1/2), u(0, t) = 0, eval(diff(u(x, t), x), x = 1) = 0]

Error, (in PDEtools:-ToJet) found functions to be rewritten in jet notation, {u(1, t)}, having different dependency than the indicated in [u(x, t)]

what is the meaning of above error and how to resolve this to get the solution from pdsolve command?

I would like to find which of my approximately 150 recorded worksheets reference the VariationalCalculus package.

Instead of tediously displaying these one at a time, is there a search mechanism that will list the names of all my worksheets containing the command with(VariationalCalculus)?

fcns:=[u(x,y,t),v(x,y,t),h(x,y,t),c(x,y,t)]:

gr:=0.5:pr:=0.71:sc:=0.7:m:=1.0:k:=0.3:
  fcns:=[u(x,y,t),v(x,y,t),h(x,y,t),c(x,y,t)]:
  IC := [u(x,y,0)=0,v(x,y,0)=0,h(x,y,0)=0,c(x,y,0)=0]:
  BC:=[u(0,y,t)=0,h(0,y,t)=0,c(0,y,t)=0,u(x,0,t)=1,v(x,0,t)=0,h(x,0,t)=1,c(x,0,t)=1,u(x,10,t)=0,h(x,10,t)=0,c(x,10,t)=0];
  eq1:={diff(u(x,y,t),t)+u(x,y,t)*diff(u(x,y,t),x)+v(x,y,t)*diff(u(x,y,t),y)=diff(u(x,y,t),y$2)+gr*h(x,y,t)+gr*c(x,y,t)-m*u(x,y,t)
,diff(h(x,y,t),t)+u(x,y,t)*diff(h(x,y,t),x)+v(x,y,t)*diff(h(x,y,t),y)=1/pr*diff(h(x,y,t),y$2),diff(c(x,y,t),t)+u(x,y,t)*diff(c(x,y,t),x)+v(x,y,t)*diff(c(x,y,t),y)=1/sc*diff(h(x,y,t),y$2)-k*c(x,y,t)}:
  pds:= pdsolve(eq1,IC,BC,fcns,numeric):
  pds:= pdsolve(eq1,IC,BC,fcns,numeric,spacestep = 1/100):

for the above problem i made this code.

How to explain the difference in the outputs of

restart; ans1 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), {x, y});
ns1 := {x = 3-sqrt(-y^2-4*y+77), -11 <= y, y < 13/25},
 {-11 < y, x < -5+sqrt(-y^2+8*y+273), y < 13/25, 3-sqrt(-y^2-4*y+77) < x}, 
{x = -5+sqrt(-y^2+8*y+273), -11 < y, y < 13/25}, {y = 13/25, -141/25 <= x, x <= 291/25},
 {x = 3-sqrt(-y^2-4*y+77), y <= 7, 13/25 < y}, 
{13/25 < y, x < 3+sqrt(-y^2-4*y+77), y < 7, 3-sqrt(-y^2-4*y+77) < x}, 
{x = 3+sqrt(-y^2-4*y+77), 13/25 < y, y < 7}

and

restart; ans2 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), [x, y]);
ans2 := [[x < 3, -6 <= x, y = -2-sqrt(-x^2+6*x+72)], 
[x < 3, -6 < x, y < -2+sqrt(-x^2+6*x+72), -2-sqrt(-x^2+6*x+72) < y], 
[x < 3, -6 < x, y = -2+sqrt(-x^2+6*x+72)], [x = 3, y <= 7, -11 <= y],
 [x <= 291/25, 3 < x, y = 4-sqrt(-x^2-10*x+264)],
 [x < 291/25, 3 < x, y < -2+sqrt(-x^2+6*x+72), 4-sqrt(-x^2-10*x+264) < y],
 [x < 291/25, 3 < x, y = -2+sqrt(-x^2+6*x+72)]]

?

In the former x is expressed through y and in the latter y is expressed through x. I find explanation  in neither ?solve nor ?solve,details.

can anyone one tell me the meaning of builtin with examples?