Annae

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These are questions asked by Annae

Hello!

How do I solve this system? could someone help me please.

restart;
eqns := {x(t+1) = (1+10^(-6)*(0.4e-2-0.6e-2)/(0.1e-3))*x(t)+0.7e-1*10^(-6)*y(t),

y(t+1) = 0.6e-2*10^(-6)*x(t)/(0.1e-3)+(1-0.7e-1*10^(-6))*y(t)};

with:
x(0) = 1
y(0) =
y(0) = 857.1428571

restart

eqns := {x(t+1) = (1+10^(-6)*(0.4e-2-0.6e-2)/(0.1e-3))*x(t)+0.7e-1*10^(-6)*y(t), y(t+1) = 0.6e-2*10^(-6)*x(t)/(0.1e-3)+(1-0.7e-1*10^(-6))*y(t)};

{x(t+1) = .9999800000*x(t)+0.7000000000e-7*y(t), y(t+1) = 0.6000000000e-4*x(t)+.9999999300*y(t)}

(1)

x(0) = 1

x(0) = 1

(2)

y(0) = 0.6e-2/(0.1e-3*0.7e-1)

y(0) = 857.1428571

(3)

``

Download SystemRecursive.mw

Hello!

How do I get the plot of P(t) and C(t) and also a table with the values of P(t) for each t? Itried but I couldn't...

``

restart; beta := 0.7e-2; Lambda := 0.2e-4; `ρ__o` := 0.3e-2; lambda := 0.8e-1; h := 0.1e-1; n := 100

Error,

restart; beta := 0.7e-2; Lambda := 0.2e-4; `ρ__o` := 0.3e-2; lambda := 0.8e-1; h := 0.1e-1; n := 100

 

for i from 0 to n-1 do P[i+1] := (1+h*(`ρ__o`-beta)/Lambda)*P(i)+h*lambda*C(i); C[i+1] := h*beta*P(i)/Lambda+(-h*lambda+1)*C(i) end do:

seq(i, i = 0 .. 30); seq(P[i], i = 0 .. 30)

Error,

seq(i, i = 0 .. 30); seq(P[i], i = 0 .. 30)

 

with(plots); with(DEtools); p1 := plot([P(t)], t = 0 .. 100, [[P(0) = 1]], scene = [t, P(t)], thickness = 2, linecolor = red, stepsize = .1); p2 := plot([C(T)], t = 0 .. 100, [[C(0) = beta/(Lambda*lambda)]], scene = [t, C(t)], thickness = 2, linecolor = red, stepsize = .1); display([p1, p2])

``

Download System_Recursive_Equations.mw

Thank!!!

Hello!

how to find the solutions of a system of recursive equations? And the plot too.

I tried but...

B := rsolve({a(0) = 0, a(i) = (1 + 10^(-5)*(0.01*(i - 1) - 0.007)/0.0001)*a(i - 1) + 0.1*10^(-5)*c(i - 1), c(0) = 0, c(i) = 0.01*10^(-5)*(i - 1)/0.0001*a(i - 1) + (1 - 10^(-5))*0.1*c(i - 1)}, {a(i), c(i)}, 'genfunc'(t));
B := rsolve({a(i) = (0.9983000000 + 0.001000000000 i) a(i - 1)

   + 0.000001000000000 c(i - 1), 

  c(i) = 0.001000000000 (i - 1) a(i - 1) + 0.09999900000 c(i - 1)

  }, {a(i), c(i)}, genfunc(t))

rsolve_for_system_of_recursive_equations.mw

thanks

Equação26_12.mw

Download Equação26_12.mw

Hello!

How can i get datas and graphs of implicit function. I tried...

with(DEtools, odeadvisor);

ode := diff(y(x), x) = (-0.1*(y(x) - 0.7)^3 - 0.8*y(x)*(y(x) - 0.7)^2)/(0.7^2 - 2*0.7*y(x) + y(x)^2 - 0.7*0.2*0.8);
                                    3                        2
         d         -0.1 (y(x) - 0.7)  - 0.8 y(x) (y(x) - 0.7) 
 ode := --- y(x) = -------------------------------------------
         dx                                        2          
                            0.378 - 1.4 y(x) + y(x)           
odeadvisor(ode);
          /                            3                        2\
          | d         -0.1 (y(x) - 0.7)  - 0.8 y(x) (y(x) - 0.7) |
odeadvisor|--- y(x) = -------------------------------------------|
          | dx                                        2          |
          \                    0.378 - 1.4 y(x) + y(x)           /
ans := dsolve(ode, implicit);
                2        9                    199                
ans := x + ----------- + -- ln(10 y(x) - 7) + --- ln(90 y(x) - 7)
           10 y(x) - 7   28                   252                

   + _C1 = 0
ic1 := y(0) = 0;
                        ic1 := y(0) = 0
sol := dsolve([ode, ic1], implicit);
                2        9                    199                
sol := x + ----------- + -- ln(10 y(x) - 7) + --- ln(90 y(x) - 7)
           10 y(x) - 7   28                   252                

     2   10         10         
   + - - -- ln(7) - -- I Pi = 0
     7   9          9          
subs(x = 1, sol);
   9        2        9                    199                
   - + ----------- + -- ln(10 y(1) - 7) + --- ln(90 y(1) - 7)
   7   10 y(1) - 7   28                   252                

        10         10         
      - -- ln(7) - -- I Pi = 0
        9          9          
solve(9/7 + 2/(10*y(1) - 7) + (9*ln(10*y(1) - 7))/28 + (199*ln(90*y(1) - 7))/252 - (10*ln(7))/9 - 10*I*Pi/9 = 0, y(1));
1     /      /                                                  
-- exp|RootOf|-280 I Pi exp(_Z) - 280 ln(7) exp(_Z) + 15680 I Pi
90    \      \                                                  

          /1           56\                                       
   + 81 ln|- exp(_Z) - --| exp(_Z) + 199 _Z exp(_Z) + 15680 ln(7)
          \9           9 /                                       

                          /1           56\                   \\
   + 324 exp(_Z) - 4536 ln|- exp(_Z) - --| - 11144 _Z - 13608||
                          \9           9 /                   //

     7 
   + --
     90
implicitplot(sol, x = 0 .. 10, y = 0 .. 10);
                /         2        9                 
    implicitplot|x + ----------- + -- ln(10 y(x) - 7)
                \    10 y(x) - 7   28                

         199                   2   10         10           
       + --- ln(90 y(x) - 7) + - - -- ln(7) - -- I Pi = 0, 
         252                   7   9          9            

                              \
      x = 0 .. 10, y = 0 .. 10|
                              /
but I wasn't successful.

Thanks

Hi!

How do I solve a equation ln in Maple:ln.mw


 

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