MaplePrimes Questions

Hi,

I am the administrator of Maple in my school, and all the students use Maple in part of their exams. Is it possible  to block the access to ChatGPT thru eg. the firewall or otherwise during exams. 

The reason for this question is that the students must have access to some internet sources during exams, but definately not CharGPT.

Kind regards 

Per Kirkegaard

Hello, I try to solve the equations of the odometric model with the Maple 2024 but I have not the answers as with the hands, can you help me to verify it ?

dsolve(diff(phi(t), t) = tan(10*t)/5)

dsolve(diff(x(t), t) = V*cos(ln(1 + tan(10*t)^2)/100))

dsolve(diff(y(t), t) = V*sin(ln(1 + tan(10*t)^2)/100))

Best regards, Edern Ollivier.

I noticed that Student:-ODEs:-ODESteps does not use the newer subscripted constant of integrations for solution of odes which looks much nicer.

Is there a way to make it use same constant of integrations as dsolve() does? Compare  

This is on a worksheet using typesetting level extended. Worksheet is attached


 

restart

18836

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1724 and is the same as the version installed in this computer, created 2024, April 15, 17:29 hours Pacific Time.`

#to make Maple use the new constant of integrations. Is this still needed in Maple 2024?
dsolve(diff(y(x),x$9)=1,arbitraryconstants=subscripted):
pdsolve(diff(psi(x,t),x$9)=0,arbitraryfunctions=subscripted):

ode := diff(y(x), x$2) + 2*y(x) = 0;
Student:-ODEs:-ODESteps(ode,y(x));

ode := diff(y(x), x, x)+2*y(x) = 0

"[[,,"Let's solve"],[,,((ⅆ)^2)/(ⅆx^2) y(x)+2 y(x)=0],["•",,"Highest derivative means the order of the ODE is" 2],[,,((ⅆ)^2)/(ⅆx^2) y(x)],["•",,"Characteristic polynomial of ODE"],[,,r^2+2=0],["•",,"Use quadratic formula to solve for" r],[,,r=(0+/-([]))/2],["•",,"Roots of the characteristic polynomial"],[,,r=(-ⅈ sqrt(2),ⅈ sqrt(2))],["•",,"1st solution of the ODE"],[,,y[1](x)=cos(sqrt(2) x)],["•",,"2nd solution of the ODE"],[,,y[2](x)=sin(sqrt(2) x)],["•",,"General solution of the ODE"],[,,y(x)=C1 y[1](x)+C2 y[2](x)],["•",,"Substitute in solutions"],[,,y(x)=C1 cos(sqrt(2) x)+C2 sin(sqrt(2) x)]]"

#compare to this output
dsolve(ode,y(x));

y(x) = c__1*sin(2^(1/2)*x)+c__2*cos(2^(1/2)*x)


 

Download make_step_solution_use_new_constant_of_integration.mw

 

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance. 

123.mw

 

 

 

 

restart

C_m := 1.0; g_K := 36.0; I_inj := 0; g_L := .3; E_Na := 50.0; E_K := -77.0; E_L := -54.4

alpha_m := (.1*(V-25.0))/(1-exp(-(V-25.0)*(1/10))); beta_m := 4*exp(-V/(18.0)); alpha_h := 0.7e-1*exp(-V/(20.0)); beta_h := 1/(1+exp(-(V-30)*(1/10))); alpha_n := (0.1e-1*(V-10.0))/(1-exp(-(V-10.0)/(10.0))); beta_n := .125*exp(-V/(80.0)); I_Na := g_Na*m^3*h*(V-E_Na); I_K := g_K*n^4*(V-E_K); I_L := g_L*(V-E_L)

.125*exp(-0.1250000000e-1*V)

(1.1)

eq1 := (I_inj-I_Na-I_K-I_L)/C_m; m := alpha_m/(alpha_m+beta_m); n := alpha_n/(alpha_n+beta_n); h := alpha_h/(alpha_h+beta_h)

-16.32000000-1.000000000*g_Na*m^3*h*(V-50.0)-36.00000000*n^4*(V+77.0)-.3000000000*V

 

.1*(V-25.0)/((1-exp(-(1/10)*V+2.500000000))*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V)))

 

0.1e-1*(V-10.0)/((1-exp(-.1000000000*V+1.000000000))*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V)))

 

0.7e-1*exp(-0.5000000000e-1*V)/(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))

(1.2)

bif_eq1 := eq1 = 0;

-16.32000000-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.3600000000e-6*(V-10.0)^4*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000*V = 0

bif_eq2 := diff( eq1, V) = 0;

-0.2100000000e-3*g_Na*(V-25.0)^2*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*exp(-(1/10)*V+2.500000000)/((1-exp(-(1/10)*V+2.500000000))^4*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-3*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(.1/(1-exp(-(1/10)*V+2.500000000))-0.1000000000e-1*(V-25.0)*exp(-(1/10)*V+2.500000000)/(1-exp(-(1/10)*V+2.500000000))^2-.2222222222*exp(-0.5555555556e-1*V))/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^4*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.3500000000e-5*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(-0.3500000000e-2*exp(-0.5000000000e-1*V)+(1/10)*exp(-(1/10)*V+3)/(1+exp(-(1/10)*V+3))^2)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))^2)-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.1440000000e-5*(V-10.0)^3*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-6*(V-10.0)^4*(V+77.0)*exp(-.1000000000*V+1.000000000)/((1-exp(-.1000000000*V+1.000000000))^5*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-5*(V-10.0)^4*(V+77.0)*(0.1e-1/(1-exp(-.1000000000*V+1.000000000))-0.1000000000e-2*(V-10.0)*exp(-.1000000000*V+1.000000000)/(1-exp(-.1000000000*V+1.000000000))^2-0.1562500000e-2*exp(-0.1250000000e-1*V))/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^5)-0.3600000000e-6*(V-10.0)^4/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000 = 0

 

 

 

bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

Warning, solutions may have been lost

 

 

as the solutions, which are then expressed as the points mu, y via

   

[Back to ODE Powertool Table of Contents]

 

 

Can a plot be output to a pixel array?                                                  

Is there a way to disable Maples AI Formula Assistant? This could be relevant when using Maple for a test.

Given this simplified solution, 

sol1 := (-vin + sqrt(-4*I2^2*R^2 + vin^2))/(2*I2*omega0*L)

how do I bring the denominator back under the radical?

I have solution to system of equations that results (I assign it to) in:

I2sol := -I*omega0*k*L*vin*1/(L^2*k^2*omega0^2 + R^2)

I then try to solve it for k by doing

solve(I2sol = I2, k)

but that doesn't work.  What is the "right" Maple way to rearrange I2 such that the expression is the solution(s) for k?

I want to make the system of ODE into its dimensionless version:

Dimensional version: 

dN/dT= R*N (1 −N/K)−alpha*N*P/(A + N);

dP/dT= gamma*N*P/( A + N) + C*P/(1 + Q*P) −MP;

N (0) ≡N_0 ≥0 and P (0) ≡P_0 ≥0

R, K alpha, gamma, M, C, Q are all positive constant. 

Using one choice of dimensionless variable x = N/K , y = alpha*P/(R*K), t = R*T, the system of ODE can be reduced to its dimensionless version as follows:

dx/dt = x*(1 −x ) −x*y/(a + x);

dy/dt = b*x*y/(a + x) + c*y/(1 + q*y) −m*y

where the dimensionless parameters are a = A/K , b = gamma/R , c = C/R , q = Q*R*K/alpha, and m = M/R.

How to do this in maple. Please help. 

How to integrate the below term

int((n*p+exp(n*p))*exp(-p)*p^(s-1)*f^s/((n*p+exp(2*n*p))*factorial(s)), p = 0 .. 1);
eval(%);

Hey! I need help ASAP, because my maple file has been corrupted and i dont know what to do. Do you guys know how to recover a file? i can save it again as_mw. but should i change it to xml? or how? i have the link to my maple file attached, so if someone can help me, it could be helpful! Because i have an upcoming exam. Thanks youu

I noticed tags on the post  

https://mapleprimes.com/questions/238161-Why-Maple-Gives-Solution-To-Euler-Ode

keep disappearing. 

I added tags "differential equation" and "dsolve" and so on.  

Later on when I visit this site again I found the tags are all gone.

Why does Mapleprimes remove the tags on post?

Or is someone else removing the tags? If so, why? is something wrong with the tags I've added?

This happend twice on this one post. I noticed earlier today the tags were gone, so I added them again. And now I see the same thing. They are all gone.

How could I find the volume of this equation (x^2+y^2+z^2+12)^2=64(x^2+y^2) using triple integrals in both spherical and cylindrical coords ? Thank you !

I found that sometimes Maple gives

               Error, (in Typesetting:-Parse) too many levels of recursion

When using the Latex command on the output of Student:-ODEs:-ODESteps

Below is worksheet showing it works for some and gives error for others. Is there a workaround for this? I'd like to convert the steps to Latex.

This happens in worksheet using either Display->Typesetting level as EXTENDED or STANDARD

restart;

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1722 and is the same as the version installed in this computer, created 2024, April 12, 17:58 hours Pacific Time.`

ode:=diff(y(x),x)=0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(y(x), x) = 0

\begin{array}{ccc}
 & {} & \textrm{Let's solve}
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)=0
\\
 \textrm{•} & {} & \textrm{Highest derivative means the order of the ODE is}1
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)
\\
 \textrm{•} & {} & \textrm{Integrate both sides with respect to}x  
\\
 {} & {} & \int \left(\frac{d}{d x}y \! \left(x \right)\right)d x =\int 0d x +\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Evaluate integral}
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Solve for}y \! \left(x \right)
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\end{array}

ode := diff(y(x), x, x, x ) + 3*diff(y(x), x, x) + 4*diff(y(x), x) + 2*y(x) = 0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(diff(diff(y(x), x), x), x)+3*(diff(diff(y(x), x), x))+4*(diff(y(x), x))+2*y(x) = 0

Error, (in Typesetting:-Parse) too many levels of recursion

 


 

Download latex_error_ODE_steps_maple_2024_april_13_2024.mw

 

update: Reported to Maplesoft support.

 

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