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Hi all,

By solving cubic equation in maple (version 17), I got



-0.363700352e-2*y^3-.4041941000*y^2+3.397775673*y-2.377540486 = 0

-0.363700352e-2*y^3-.4041941000*y^2+3.397775673*y-2.377540486 = 0



[[y = .7709248124], [y = 7.123944371], [y = -119.0286907]]



Now I want to find these roots through the formula.


I solve it generally in Maple.. 


``# Suppose

A*y^3+B*y^2+C*y+E = 0

A*y^3+B*y^2+C*y+E = 0



A := -0.363700352e-2:

B := -.4041941000:

C := 3.397775673:

E := -2.377540486:


A*y^3+B*y^2+C*y+E = 0


A*y^3+B*y^2+C*y+E = 0



y1 := (1/6)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A-(2/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3))-(1/3)*B/A






y2 := y = -(1/12)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(1/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3))-(1/3)*B/A+(1/2*I)*sqrt(3)*((1/6)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(2/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)))

y = 22.91263477*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+18.37098733/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)-37.04460717+((1/2)*I)*3^(1/2)*(-45.82526955*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+36.74197467/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3))



y = .770924807+0.1772050808e-7*I


y3 := y = -(1/12)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(1/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3))-(1/3)*B/A-(1/2*I)*sqrt(3)*((1/6)*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)/A+(2/3)*(3*A*C-B^2)/(A*(-108*E*A^2+36*A*B*C+12*sqrt(3)*sqrt(27*A^2*E^2-18*A*B*C*E+4*A*C^3+4*B^3*E-B^2*C^2)*A-8*B^3)^(1/3)))

y = 22.91263477*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+18.37098733/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)-37.04460717-((1/2)*I)*3^(1/2)*(-45.82526955*(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3)+36.74197467/(.7114884222-(0.5542993294e-1*I)*3^(1/2))^(1/3))



y = 7.123944373-0.1692050808e-7*I



y1, y2, y3 formulas are computed by Maple by solving it for general formula.
But, now I got answers in real and imaginery parts, i.e


y1 = -119.0286907-1.*10^(-9)*I

y2 = .770924807+1.772050808*10^(-8)*I

y3 = 7.123944373-1.692050808*10^(-8)*I


Why, is it so?



I want answers in simple forum directly only by using these formulas. As i have to show the proof!

Thanks in advance




Dear all,

Thanks for your answer. I have a simple question:

Let A be a Matrix, X[1] and X[2] two vectors.

I have this equation:  X[2]= X[1]+ A*X[1]+A*X[2];  Using Maple how can I  writte X[2] =P*X[1]; where P is a matrix to be founded.

Here, P:=(Id-A)^(-1)*A; But how using maple.






I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:

dy/dx = (x^2) - (2y^2) - C = 0

This is what I had so far:







'Function'(x,y) = Function(x,y);





This is only display one family. How do I code for it plot the other families?

(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)

Please help.

hi, I am new here I want to solve these toe coupled equations with the following boundary condition numerically:

  1)  diff(f(eta),eta$3)+(1)/(2)*f(eta)*diff(f(eta),eta$2)-xi*(2*f(eta)*(diff(f(eta),eta))*



2)   diff(theta(eta),eta,eta)+(1)/(2)*Pr*f(eta)*(diff(theta(eta),eta))=0

boundary conditions: 1)  f(0) = 0   2)  D(f)(0) = 0   3)  D(f)(infinity=10) = 1

                               1) theta(infinity=10) = 1      2) theta(0)=0

xi=0.2 ... 1    K=0.2     pr=0.7

AOA... I want to convert system of equations into matirx form.

F[0] := u[0, n]-u[0, n-1]+u[1, n]-u[1, n-1]+u[2, n]-u[2, n-1]+u[3, n]-u[3, n-1]

F[1] := u[0, n]-u[0, n-1]-u[1, n]+u[1, n-1]+u[2, n]-u[2, n-1]-u[3, n]+u[3, n-1];

F[2] := u[0, n]/P-u[0, n-1]/P-.7071067810*u[1, n]/P+.7071067810*u[1, n-1]/P+.7071067810*u[3, n]/P-.7071067810*u[3, n-1]/P+0.4549512860e-1*exp(-1.*t)-.3431457508*u[2, n]+.3431457508*u[2, n-1]+1.556349186*u[3, n]-1.556349186*u[3, n-1] = 0;

F[3] := u[0, n]/P-u[0, n-1]/P-.7071067810*u[1, n]/P+.7071067810*u[1, n-1]/P+.7071067810*u[3, n]/P-.7071067810*u[3, n-1]/P+0.4549512860e-1*exp(-1.*t)-.3431457508*u[2, n]+.3431457508*u[2, n-1]+1.556349186*u[3, n]-1.556349186*u[3, n-1] = 0;

I want to export the above system of equation in to matrices of as

AU[n]+BU[n-1]-C = O;

where*U[n] = Typesetting[delayDotProduct](Vector(4, {(1) = u[0, n], (2) = u[1, n], (3) = u[2, n], (4) = u[3, n]}), a, true)*n*d*U[n-1] and Typesetting[delayDotProduct](Vector(4, {(1) = u[0, n], (2) = u[1, n], (3) = u[2, n], (4) = u[3, n]}), a, true)*n*d*U[n-1] = (Vector(4, {(1) = u[0, n-1], (2) = u[1, n-1], (3) = u[2, n-1], (4) = u[3, n-1]})), Help me plz;

Is it possible to find all the solutions of the equation

abs(tan(x)*tan(2*x)*tan(3*x))+abs(tan(x)+tan(2*x)) = tan(3*x)

which belong to the interval 0..Pi with Maple?



Hi, the title isn't great as I didn't know how to describe this really. I need to solve the following equation for b:

y = (1-exp(-x*b))/(1-exp(-50*b))

When I put a value for y in, this is fine and fsolve gives me a numeric real solution. However, even when using RealDomain, it does not give me a real solution if I leave y as it is, and instead gives a 'RootOf' solution, which I don't really understand. This is the same whether using solve or isolate:


I have the values of x and y for multiple data points and can put them in an nx1 matrix. Is there a way to replace x and y with matrices (with real numbers in) and solve for each set of points for b (ie there would be n values of b)? Obviously I could go through and put in each value of x and y but this would take ages, so was just wondering if there's a quick way to do this.

I have tried by simply putting matrices instead of the letter but get the error:

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received Vector(50, {(1) = -50*b, (2) = -49*b,...

Thanks for your time


I have the following nonlinear Differential Equation and don't know how to solve.  Can anyone give me any hints on how solvle for E__fd(t).  I don't even know the specific classification (other than nonlinear) of this DE can someone at least give me hint on that. Thanks.


.5*(diff(E__fd(t), t)) = -(-.132+.1*e^(.6*E__fd(t)))*E__fd(t)+0.5e-1




Can anyone tell me how to solve the equation above using Maple.  I know that there is a solution around x=0.995, y=0.743, but I cannot induce Maple to find it.  Any help or suggestions would be appreciated.



Hi there,

I'm quite new to Maple so please forgive me! I have a system of partial differential equations I'm trying to solve in Maple as such below 


df/dt = f(1-f) - f * h

dg/dt = g(1-g) * Gradient(1-f * gradient(g))

dh/dt = (g - h) + Laplacian(h),

where f,g,h are functions of space and time (i.e. f(x,y,z,t)). I guess my first question is - is this possible in Maple to evaluate? (I'm currently unsure on ICs as I'm figuring it out from the model - it's a model for cancer growth I'm trying to evaluate but have a rough idea of what I'd use).

If it is possible, can you please share how I'd write this? Everytime I've tried I seem to be failing to define anything properly, so your expertise would be greatly appreciated!


So I have two simultaneous equations, 

T= n1/(1+|T-S|) and S=n2/(n3+|T-S|) 

Where n1, n2 and n3 are constant parameters (from here on I fix n1=1 and n3=0.3). So I want to plot T, S against n2 for different values of n2. 

If I also fix n2 (say, n2=1.5) I  can get values for T and S no problem. 

But I've no idea (after many hours of searching) how to progresss. I know I need the program to put various values of n2 into the two equations and then plot the solutions numerically but I'm unsure what to try next.

Could anyone please shed some light on this?!


How can I get solution of  the following equation of orbit for schwarzschild BH in form of Jacobi Elliptical Integrals on Maple 12 platform,

diff(r(phi), phi) = r^2*sqrt(e^2-(1-2*M/r)*(1+l^2/r^2))/l

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).


However, when I try to add:



I no longer get a solution.


Any guidance would be appreciated.




I have uploaded a worksheet with the equations...


Can we define/set a range in Maple. e.g 

I have the following equation:

y = 1.048 + 1.02*x + 6.118*(z-4.041*x^2) + 16.22*(z^2) +6.241* (x*z)

The value of z is within 0.001 - 0.543, y is from 1 - 12 and x is from 0.001 - 0.7

How should I define it in Maple, so while solving equations it read the values within the given range? 

i have got alot of mixed and high degree derivatives. For example:

u[x]*u[x,t]*eta[x,t]+u[]^2*u[x]*eta[x]+kis(x,y)u[x,t]^2*u[]+eta(x, y)*u[]*u[x]^2+ksi[x,t]*u[x]^2*u[x,t]+......

like this alot of terms

my question is how can i solve divided by the derivative of the u(x,t) partial differential equations system and so  how can i find eta(x,t,u) and ksi(x,t,u) 

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