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    unforgiven_davs's Avatar
    unforgiven_davs Posts: 1, Reputation: 1
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    #1

    Apr 28, 2012, 12:32 PM
    Calculation system of differential equations in mathcad
    I would like to learn to solve system of differential equation in MathCad like this one:
    dI(t)/dt = coeff * I(t) * S(t)

    dS(t)/dt = -coeff * I(t) * S(t)

    N = S(t) + I(t)

    where 'N' and 'coeff' are user specified coefficients

    In MathCad I did:
    ( coeff * y0 * y1 )
    D(t, y) := ( )
    ( -coeff * y0 * y1 )

    ( 1 )
    ic := ( )
    ( 9 )

    But :
    S := rkfixed (ic, 0, 10, 100, D)

    returns: D - this function can't be used here.

    And I don't know how and where insert N=S(t) + I(t) equation :(
    Chic_Bowdrie's Avatar
    Chic_Bowdrie Posts: 54, Reputation: 8
    Junior Member
    		  
    #2

    May 15, 2012, 12:13 PM
    I don't have MathCad, but the solution is straight forward by substituting S = N - L into the deritative equation dL/dt. Separate the variables, L on one side and dt on the other, then integrate both sides of the following:



    C is the coeff in your differential equations. The integration gives you t as a function of the log of L. The solution for L is



    where x is an integration constant. Do the same for dS/dt and you get
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