1
$\begingroup$

I have a system of differential equation for which I want analytical solution. Let say my equations are -

x'[t] - X[[i]]*y[t] == 0, 
y'[t] + X[[i]]*x[t] == 0

where X = [0.11, 0.21, 0.31, 0.41]

How can I write a for loop such that it takes X[[i]] from X and find the analytical solution and print/plot it?

I am trying following -

For[i = 1, i < 5,
    sols = DSolve[{x'[t] - X[[i]]*y[t] == 0,
                   y'[t] + X[[i]]*x[t] == 0}, x[0] == 1, y[0] == 0, {x, y}, t]
   ];

Unfortunately, it isn't working.

$\endgroup$

3 Answers 3

2
$\begingroup$
c = Range[11, 41, 10]/100;
sol = Table[
   DSolveValue[{x'[t] - c[[i]]*y[t] == 0, y'[t] + c[[i]]*x[t] == 0, 
     x[0] == 1, y[0] == 0}, {x[t], y[t]}, t], {i, Length@c}];
Plot[sol, {t, 0, 60}, PlotLegends -> "Expressions", 
 ImageSize -> Large]

enter image description here

$\endgroup$
3
  • $\begingroup$ Thanks @Okkes Dulgerci. Could you please tell how to export solutions x[t] and y[t] separately in different files. $\endgroup$
    – luv_phy
    Apr 5, 2018 at 13:57
  • $\begingroup$ x[t]=sol[[All,1]] and y[t]=sol[[All,2]] $\endgroup$ Apr 5, 2018 at 14:05
  • $\begingroup$ Or {x[t],y[t]}=Transpose@sol $\endgroup$ Apr 5, 2018 at 14:07
1
$\begingroup$
coefs = {0.11, 0.21, 0.31, 0.41}
DSolve[{x'[t] - #*y[t] == 0, y'[t] + #*x[t] == 0, x[0] == 1, 
    y[0] == 0}, {x, y}, t] & /@ coefs
$\endgroup$
1
$\begingroup$
X = {0.11, 0.21, 0.31, 0.41} 
sols = {};
For[i = 1, i < 5, i++, 
AppendTo[sols,DSolve[{x'[t] - X[[i]]*y[t] == 0, y'[t] + X[[i]]*x[t] == 0, x[0] == 1, y[0] == 0}, {x[t], y[t]}, t]]];
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.