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solving first order DE

  • 03-12-2008 11:13pm
    #1
    subzero12
    Closed Accounts Posts: 96 ✭✭


    the question asks
    solve first order DE

    dx/dt= -.03X

    X(0)=3

    which means
    X(t) 3e^-.3t

    which i can do
    so it ask for what are X(2)
    which is -.3*2= -.6
    so then you do 3*e-.6 =1.646

    the next part i dont understand
    it as for
    find the time t when X(t)=1
    what do i do to get this i know its probably really simple i just cant get my head around it .
    thanks for any help in advance


Comments

  • #2
    LeixlipRed
    Closed Accounts Posts: 6,081 ✭✭✭LeixlipRed


    So you want the value of t that corresponds to X(t)=1. So you need to solve for t given that X(t)=1. Can you see what I mean?


  • #3
    subzero12
    Closed Accounts Posts: 96 ✭✭subzero12


    ok so i think i understand
    1/3 = .333

    so i take ln.333 =-1.099612

    so we have -.3t=-1.099612

    then t = -1.099612/3 =3.66

    am i on the right track ?


  • #4
    Cokehead Mother
    Closed Accounts Posts: 773 ✭✭✭Cokehead Mother


    I got t = (10ln3)/3 = 3.66 too anyway.

    3e^-.3t = 3e^{(-.3/3)(10ln3)} = 3e^{-ln3} = 3/e^{ln3} = 3/3 = 1. Seems fine.


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