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How do I solve the following system of ODE's?

$\qquad \frac{dx}{dt}=\{-(n+1)r_1+(m+1/2)r_2\}x+n\,r_1y$

$\qquad \frac{dy}{dt}=-\{(n\,r_1+(m+1/2)r_2\}y+(n+1)r_1x$

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    $\begingroup$ Please show the differential equation in source form, so we can copy-paste it into Mathematica and try to help you. $\endgroup$
    – Roman
    Feb 22, 2019 at 6:55
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    $\begingroup$ To the downvoters: Note that rabia is new contributor. You should allow new contributes some time to adjust to the spirit of the forum and fix their post. Please read the Code of Conduct and try to be excellent to each other! I upvoted the question justy because too many downvoted it. $\endgroup$
    – user21
    Feb 22, 2019 at 9:21
  • $\begingroup$ @user21 Good point. I took away mine so as to not discourage someone who has no reason to know the semi-obscure rules that we've all absorbed over time. $\endgroup$
    – b3m2a1
    Feb 22, 2019 at 10:46
  • $\begingroup$ @b3m2a1, thanks! $\endgroup$
    – user21
    Feb 22, 2019 at 12:12

1 Answer 1

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As a new user you should check the documentation on DSolve

Eq1 = x'[t] == (-(n + 1)*r1 + (m + 1/2)*r2)*x[t] + n*r1*y[t]

Eq2 = y'[t] == -(n*r1 + (m + 1/2)*r2)*y[t] + (n + 1)*r1*x[t]

Sol = DSolve[{Eq1, Eq2}, {x[t], y[t]}, t] // FullSimplify

If you are looking for a particular solution then you need to provide boundary conditions?

If you are looking for a numerical solution then you need to provide numerical values to the different parameters as well as bcs and for this you need to use NDSolve?

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  • $\begingroup$ thank you so much, its really help me. $\endgroup$ Feb 23, 2019 at 7:20
  • $\begingroup$ @rabiarajpoot try it and feel free to ask $\endgroup$
    – zhk
    Feb 23, 2019 at 7:21
  • $\begingroup$ yes,I have already try this and get solution.thanku $\endgroup$ Feb 23, 2019 at 7:24

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