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Homework Help: General solution of differential equation system

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of the system of differential equations
    [tex]x'=10x - 12y[/tex]
    [tex]y'=25x - 30y[/tex]
    (where primes indicate derivatives with respect to t) by using the initial conditions

    2. Relevant equations

    3. The attempt at a solution

    [tex]x''=10x' - 12y'[/tex]
    [tex]x(t)=Ae^{-20t} +B[/tex] [tex]\rightarrow[/tex] [tex]x(0)=A[/tex]
    [tex]y=\frac{10x-x'}{12}=\frac{5}{2}Ae^{-20t} \rightarrow [tex]y(0)=B[/tex]

    If A=0 and B=0, then my general solutions x(t),y(t)=0. This is clearly not right. What am I doing wrong? Thanks!
  2. jcsd
  3. Oct 29, 2009 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Use C and D in your general solution so they don't get mixed up with the A and B in the initial conditions.
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