suvetha2000

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MaplePrimes Activity


These are replies submitted by suvetha2000

@Carl Love Thank you so much, for all your help means alot. I really appreciate your help. Thank you 

@Carl Love Thank you, I was getting stuck trying to calculate it by hand, but I hope the method with maple helps be get through them. Also, is there anyway I could use Maple to convert an equation into a matrix form? As Im not sure whether my matrix form is correct. 

@tomleslie Thank you so much, so other than that I used a longer method to plot, my solutions are correct? As I was concerned as a and b had the same graph, c and d had the same graph. 

@Carl Love Thank you, I think I need to show my step by step calculation by hand and then use Maple to plot the direction field


 

restart

NULL

with(DEtools), with(linalg)

sys := {diff(x(t), t) = -y(t)+0*x(t), diff(y(t), t) = 0*y(t)+x(t)}

{diff(x(t), t) = -y(t), diff(y(t), t) = x(t)}

(1)

A := [[0, 1], [-1, 0]]

[[0, 1], [-1, 0]]

(2)

charploy(A, k)

charploy([[0, 1], [-1, 0]], k)

(3)

eigenvalues(A)

I, -I

(4)

sol := dsolve(sys)

{x(t) = _C1*sin(t)+_C2*cos(t), y(t) = -_C1*cos(t)+_C2*sin(t)}

(5)

DEplot(sys, [y(t), x(t)], t = -10 .. 10, y = -10 .. 10, x = -10 .. 10, stepsize = .1)

 

NULL

NULL

with(DEtools), with(linalg)

sys := {diff(x(t), t) = -y(t)-.25*x(t), diff(y(t), t) = 0*y(t)+x(t)}

{diff(x(t), t) = -y(t)-.25*x(t), diff(y(t), t) = x(t)}

(6)

A := [[0, 1], [-1, 0]]

[[0, 1], [-1, 0]]

(7)

charploy(A, k)

charploy([[0, 1], [-1, 0]], k)

(8)

eigenvalues(A)

I, -I

(9)

sol := dsolve(sys)

{x(t) = -(1/8)*exp(-(1/8)*t)*(3*7^(1/2)*sin((3/8)*7^(1/2)*t)*_C2-3*7^(1/2)*cos((3/8)*7^(1/2)*t)*_C1+sin((3/8)*7^(1/2)*t)*_C1+cos((3/8)*7^(1/2)*t)*_C2), y(t) = exp(-(1/8)*t)*(sin((3/8)*7^(1/2)*t)*_C1+cos((3/8)*7^(1/2)*t)*_C2)}

(10)

DEplot(sys, [y(t), x(t)], t = -10 .. 10, y = -10 .. 10, x = -10 .. 10, stepsize = .1)

 

``

NULL

with(DEtools), with(linalg)

sys := {diff(x(t), t) = -y(t)-1.5*x(t), diff(y(t), t) = 0*y(t)+x(t)}

{diff(x(t), t) = -y(t)-1.5*x(t), diff(y(t), t) = x(t)}

(11)

A := [[0, 1], [-1, 0]]

[[0, 1], [-1, 0]]

(12)

charploy(A, k)

charploy([[0, 1], [-1, 0]], k)

(13)

eigenvalues(A)

I, -I

(14)

sol := dsolve(sys)

{x(t) = -(1/4)*exp(-(3/4)*t)*(sin((1/4)*7^(1/2)*t)*7^(1/2)*_C2-cos((1/4)*7^(1/2)*t)*7^(1/2)*_C1+3*sin((1/4)*7^(1/2)*t)*_C1+3*cos((1/4)*7^(1/2)*t)*_C2), y(t) = exp(-(3/4)*t)*(sin((1/4)*7^(1/2)*t)*_C1+cos((1/4)*7^(1/2)*t)*_C2)}

(15)

DEplot(sys, [y(t), x(t)], t = -10 .. 10, y = -10 .. 10, x = -10 .. 10, stepsize = .1)

 

``

NULL

with(DEtools), with(linalg)

sys := {diff(x(t), t) = -y(t)-2.5*x(t), diff(y(t), t) = 0*y(t)+x(t)}

{diff(x(t), t) = -y(t)-2.5*x(t), diff(y(t), t) = x(t)}

(16)

A := [[0, 1], [-1, 0]]

[[0, 1], [-1, 0]]

(17)

charploy(A, k)

charploy([[0, 1], [-1, 0]], k)

(18)

eigenvalues(A)

I, -I

(19)

sol := dsolve(sys)

{x(t) = -(1/2)*_C1*exp(-(1/2)*t)-2*_C2*exp(-2*t), y(t) = _C1*exp(-(1/2)*t)+_C2*exp(-2*t)}

(20)

DEplot(sys, [y(t), x(t)], t = -10 .. 10, y = -10 .. 10, x = -10 .. 10, stepsize = .1)

 

``


 

Download QS1v.mw

@acer 

@Carl Love Thank you so much, I managed to solve this question and managed to get the same answer as the solution the work you don. So thank you much, but have another question which im stuck with.

@Carl Love I am really sorry for not getting back to you sooner, I had few issues which led me to be not be active here. I'm am very sorry, but I really appreciate your help. 

@Rouben Rostamian 

Thank you so much for your help, I really appreciate it.

Oh alright, I will go ahead with the other 2 parts of the questions by hand. 

 

@Rouben Rostamian  

Oh okay, so what else do I need to add inorder for me to gain all 3 marks for Qs1ci?

Also, is there any way in which I could use maple to solve for Qs1Cii?

@Rouben Rostamian  

Thank you so much.

Does that mean my graph was wrong? Do you think this work will be fine to receive all those marks?

@acer 

I have attempted on QS1Ci, though im not sure whether it is correct.


 

with(DEtools)

with(plots)

ode1 := diff(y(t), t) = (8/9)*y(t)*(1/9-y(t))

diff(y(t), t) = (8/9)*y(t)*(1/9-y(t))

(1)

dsolve(ode1, y(t))

y(t) = 1/(9+exp(-(8/81)*t)*_C1)

(2)

DEplot(ode1, y(t), t = -5 .. 5, y = -5 .. 5, arrows = line, title = "Direction Field-Example1")

 

IV1 := [y(0) = 3, y(0) = 1, y(0) = -1]

[y(0) = 3, y(0) = 1, y(0) = -1]

(3)

DEplot(ode1, [y(t)], t = -5 .. 5, y = -5 .. 5, IV1, arrows = line, title = "DirectionfField-Example1")

 

NULL


 

Download Part_A_-_QS1c_Maple.mw

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