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Math Help - frist order differential equation problem

  1. #1
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    frist order differential equation problem

    hi there i havent used differential equations for a while now and i have come across a problem which includes:

    dN2/dt=B*p(w)(N1-N2)-(1/h)*N2

    i tried the seperable method but failed then i put it in wolfram alpha and got a solution and i dont know how wolfram alpha solved it please help
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  2. #2
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    Re: frist order differential equation problem

    Quote Originally Posted by zak9000 View Post
    hi there i havent used differential equations for a while now and i have come across a problem which includes:

    dN2/dt=B*p(w)(N1-N2)-(1/h)*N2

    i tried the seperable method but failed then i put it in wolfram alpha and got a solution and i dont know how wolfram alpha solved it please help
    This is an odd looking DE. Is p(w) meant to represent p as a function of w, or p times w? Is \displaystyle N_1 a constant or a variable? If it's a variable, is it related to \displaystyle N_2?
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    Re: frist order differential equation problem

    yes p represents the energy density and is a function of w. N1 is a variable but since the differential equation is only after the change in N2 i assume that N1 will be a constant
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  4. #4
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    Re: frist order differential equation problem

    Quote Originally Posted by zak9000 View Post
    yes p represents the energy density and is a function of w. N1 is a variable but since the differential equation is only after the change in N2 i assume that N1 will be a constant
    What is w? Is it time dependent? Is N_1 time dependent? ...

    I assume B and h are constants

    CB
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    MHF Contributor chisigma's Avatar
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    Re: frist order differential equation problem

    Quote Originally Posted by zak9000 View Post
    hi there i havent used differential equations for a while now and i have come across a problem which includes:

    dN2/dt=B*p(w)(N1-N2)-(1/h)*N2

    i tried the seperable method but failed then i put it in wolfram alpha and got a solution and i dont know how wolfram alpha solved it please help
    Setting B\ p(w)\ N_{1}=a and B\ P(w)+\frac{1}{h}= b and supposing that neither a nor b depend from t the DE is...

    \frac{d N_{2}}{d t} = a - b\ N_{2} (1)

    ... where of course the variables are separable, so that is...

    \frac{d N_{2}}{a-b\ N_{2}}= dt (2)

    Kind regards

    \chi \sigma
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  6. #6
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    Re: frist order differential equation problem

    i put the equation into wolfram alpha where x=N2,K=N1
    dx/dt=B*K-B*x-x/L

    and i got the answer as:
    x(t) = c_1 e^((t (-B L-1))/L)+(B K L)/(B L+1)

    i was wondering how did it solve to get this answer?
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