## I am not able to solve these equation, can anyone ...

restart;
Pr:=0.71: n:=-1:

eta0:=0.0699;

EQ1:=diff(H(x), x ) - x*diff(F(x), x ) ;

EQ2:=(1+x^2)*diff(F(x), x\$2) + (3*x + x*F(x)-H(x))*diff(F(x), x) + F(x)^2 + G(x)^2 +2*P(x) + x*diff(P(x), x) ;

EQ3:=(1+x^2)*diff(G(x), x\$2) + (3*x + x*F(x)-H(x))*diff(G(x), x) ;

EQ4:=(1+x^2)*diff(H(x), x\$2) + (3*x + x*F(x)-H(x))*diff(H(x), x) + (1+F(x))*H(x)- diff(P(x), x);

EQ5:=(1+x^2)*diff(theta(x), x\$2) + x*(1-2*n)*diff(theta(x), x) + n^2*theta(x) - Pr*( n*F(x)*theta(x) + ( H(x)-x*F(x) )*diff(theta(x), x)  ) ;

EQ:={EQ1=0, EQ2=0,EQ3=0,EQ4=0 ,EQ5=0}:

IC:={ F(0)=0, G(0)=12, H(0)=0, theta(0)= 1, F(eta0)=0, G(eta0)=12, H(eta0)=0, theta(eta0)= 0, P(0)=0};

sol:= dsolve(EQ union IC,numeric,output=Array([0,0.0699]));

ques.mw

## Can I convert a date time string into a form I can...

This is most likely a simple question for the power users of this forum, but I do not manage to find a solution. I have date in an Excel file. The first column consists of dates (mm/dd/yyyy) and the second of time (hh:mm). I can easily concatenate both in Maple using cat("9/7/2023", "10:22") but how can I convert the obtained string into a date+time that Maple understands?

## How to solve a linear system with 7 variables and ...

I create a system of equations (with 9 linear equations and 7 variables).
I get 7 equations from the multiplication of a matrix M with a transposed vector of the 7 variables equals the transposed vector of the 7 variables. Other two simple equations are necessary because they are restrictions. Those two equations a re very simple and thave the 7 variable sin it.
To start I have been trying with fsolve but i haven't been able to solve it yet, as I also get the error: "Error, (in fsolve) number of equations, 9, does not match number of variables, 7"
Have you andy idea to solve this problem? Thanks in advance.

## Problem getting a plot the way I want through plot...

Below is the plot like I want it. The basic plot has been done with a simple plot command.

>plot(0, x = 0 .. 10, y = 0 .. 4, gridlines = true)

But the label of each axis was done manually. But I have tried to do it inside the plot command. A little help would be very appreciated.

So here is what I want the plot to look like:

Thank you in advance for the help.

Mario

## Plotting pseudospectra...

Hi everyone,

Do you know if there are some known codes for plotting pseudospectra of squared (and finite) matrices with given spectrum ?

Best,

Rachid

## What will be the range of p and q to get the plot ...

What will be the range of p and q to get the plot and to get the optimum solution?
If possible get a solution for particular value of p and q.
file attached: q1.mw

## How to find the value of constants?...

Hi all, any one help  me to find the values of constants by using given condition and then how to varify that the goiven condition varify the expression. I have found manually but want to varify through maple.

help.mw

## How can I insert L'(2) =0 and L''(2) > 0 in this l...

I have a list:
mylist := [x^4 + (-4*m - 7)*x^3 + (m + 4)*x^2 + (3*m - 5)*x, x^4 + (-4*m - 7)*x^3 + (m + 5)*x^2 + (5*m - 7)*x, x^4 + (-4*m - 7)*x^3 + (m + 5)*x^2 + (7*m - 5)*x, x^4 + (-4*m - 7)*x^3 + (2*m + 5)*x^2 + (3*m - 5)*x, x^4 + (-4*m - 7)*x^3 + (3*m + 1)*x^2 + (7*m - 10)*x, x^4 + (-4*m - 5)*x^3 + (2*m + 1)*x^2 + (7*m - 9)*x]

I use

L := map~(normal, mylist);

and get.

L := [x^4 - (4*m + 7)*x^3 + (m + 4)*x^2 + (3*m - 5)*x, x^4 - (4*m + 7)*x^3 + (m + 5)*x^2 + (5*m - 7)*x, x^4 - (4*m + 7)*x^3 + (m + 5)*x^2 + (7*m - 5)*x, x^4 - (4*m + 7)*x^3 + (2*m + 5)*x^2 + (3*m - 5)*x, x^4 - (4*m + 7)*x^3 + (3*m + 1)*x^2 + (7*m - 10)*x, x^4 - (4*m + 5)*x^3 + (2*m + 1)*x^2 + (7*m - 9)*x].

I use seq to list L[i] and diff(L[i])

[seq([L[i], diff(L[i], x)], i = 1 .. nops(L))];

and get

[[x^4 - (4*m + 7)*x^3 + (m + 4)*x^2 + (3*m - 5)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(m + 4)*x + 3*m - 5], [x^4 - (4*m + 7)*x^3 + (m + 5)*x^2 + (5*m - 7)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(m + 5)*x + 5*m - 7], [x^4 - (4*m + 7)*x^3 + (m + 5)*x^2 + (7*m - 5)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(m + 5)*x + 7*m - 5], [x^4 - (4*m + 7)*x^3 + (2*m + 5)*x^2 + (3*m - 5)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(2*m + 5)*x + 3*m - 5], [x^4 - (4*m + 7)*x^3 + (3*m + 1)*x^2 + (7*m - 10)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(3*m + 1)*x + 7*m - 10], [x^4 - (4*m + 5)*x^3 + (2*m + 1)*x^2 + (7*m - 9)*x, 4*x^3 - 3*(4*m + 5)*x^2 + 2*(2*m + 1)*x + 7*m - 9]]

How can I insert L'(2), L''(2) and solve the systems L'(2) = 0 and L''(2) > 0 to get the solutions m?
like this
[seq([L[i], diff(L[i], x), solve([L'(2) = 0,L''(2)>0],m) ], i = 1 .. nops(L))]

I also tried
[seq([L[i], diff(L[i], x), eval(diff(L[i], x), x = 2), solve([eval(diff(L[i], x), x = 2) = 0], m)], i = 1 .. nops(L))]

to obtain
[[x^4 - (4*m + 7)*x^3 + (m + 4)*x^2 + (3*m - 5)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(m + 4)*x + 3*m - 5, -41 - 41*m, {m = -1}], [x^4 - (4*m + 7)*x^3 + (m + 5)*x^2 + (5*m - 7)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(m + 5)*x + 5*m - 7, -39 - 39*m, {m = -1}], [x^4 - (4*m + 7)*x^3 + (m + 5)*x^2 + (7*m - 5)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(m + 5)*x + 7*m - 5, -37 - 37*m, {m = -1}], [x^4 - (4*m + 7)*x^3 + (2*m + 5)*x^2 + (3*m - 5)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(2*m + 5)*x + 3*m - 5, -37 - 37*m, {m = -1}], [x^4 - (4*m + 7)*x^3 + (3*m + 1)*x^2 + (7*m - 10)*x, 4*x^3 - 3*(4*m + 7)*x^2 + 2*(3*m + 1)*x + 7*m - 10, -58 - 29*m, {m = -2}], [x^4 - (4*m + 5)*x^3 + (2*m + 1)*x^2 + (7*m - 9)*x, 4*x^3 - 3*(4*m + 5)*x^2 + 2*(2*m + 1)*x + 7*m - 9, -33 - 33*m, {m = -1}]]

## How can I extract all the nonzero powers from poly...

I need to extract the list of all powers present in multivariable polynomial. For example, for x+y+x^2y^2+y^d I want to get the list [(1,0),(0,1),(2,2),(0,d)]. How to perform this?

## Need to Solve System of ODE Using RK-4...

Hello Everyone;

I need help to solve the following system using rk-4 method

restart;
NULL;
NULL;
C := 1.0;
gK := 36.0;
gNa := 120.0;
gL := 0.3;
VK := -77.0;
VNa := 50.0;
VL := -54.0;
III := 20;
alpha_n := 0.01*(v(t) + 55.0)/(1 - exp(-1.0/10.0*v(t) - 11.0/2.0));
beta_n := 0.125*exp((-v(t))/80.0 + (-1)*13.0/16.0);
alpha_m := 0.1*(v(t) + 40.0)/(1 - exp(-1.0/10.0*v(t) - 4.0));
beta_m := 4.0*exp(-1.0/18.0*v(t) - 65.0/18.0);
alpha_h := 0.07*exp((-1)*(v(t) + 65.0)/20.0);
beta_h := 1/(1.0 + exp((-v(t) + 35.0)/10.0));

dsys1 := {diff(h(t), t) = alpha_h*(1 - h(t)) - beta_h*h(t), diff(m(t), t) = alpha_m*(1 - m(t)) - beta_m*m(t), diff(n(t), t) = alpha_n*(1 - n(t)) - beta_n(t), diff(v(t), t) = III - gK*n(t)^4*(v(t) - VK) - gNa*m(t)^3*h(t)*(v(t) - VNa) - gL*(v(t) - VL), h(0) = 0.9996937394, m(0) = 0.02890553447, n(0) = 0.2445865495, v(0) = -70};

## How do I write Homotopy Perturbation method for a ...

HPM.mw

• How do I write Homotopy Perturbation method for a partial differential equation for this question in Maple?

## 1 dependent and 2 independent variables....

modifed_practice.mw

Impact of Shape-Dependent Hybrid Nanofluid on Transient Efficiency of a Fully W
et Porous Longitudinal Fin

dear sir please help me to solve the graph i given reference pdf also. i have implimented the code but getting error in ploting

Thank you

## Error using SingularValues in a procedure...

Using the SingularValues command with any output type specified causes this error

Error, (in sanity) invalid input: LinearAlgebra:-SingularValues expects value for keyword parameter output to be of type {list(identical(U,S,Vt,list)), identical(U,S,Vt,list)}, but received [U, S, Vt]

Below is a minimal example to trigger the error. Is there something wrong about how I am calling the function?

restart:
with(LinearAlgebra):

sanity := proc()
local A,U,S,Vt;
A :=RandomMatrix(3,10);
U,S,Vt := SingularValues(A, output=['U','S','Vt']);
end proc:

sanity();

## Point plot for system of nonlinear equations...

Dear Maple experts,

I have a system of several nonlinear equaitons. My code can solve it for a given parameter. But when I want to plot it, it takes too much time with no results. So, I decided to plot it for several given points. I get the answer for the points individually, but I don't know how to apply this to 'plot' command. Would you please help?

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