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Second order differential equation

  1. Dec 21, 2009 #1
    How do i solve the following equation?

    u= L*(d^2i/dt)+ (1/c)*i r* (di/dt)

    L= 1,4 mF
    C= 0,31 H
    R= 1000 ohm

    Well i have so far found the auxiliary equation:
    0,31*r^2 + 1000*r + 1/(1,4*10^-6)=0

    And the discriminant is found to be 114286. This makes the form of the solution:

    Y=c1*e^r1x + c2*e^r2x

    I have found the roots:

    r2= -2158,18

    But im stuck now and do not know what to do now.
    Last edited: Dec 21, 2009
  2. jcsd
  3. Dec 21, 2009 #2


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  4. Dec 21, 2009 #3


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    Are you sure you have written the equation correctly? As written, it is not a constant coefficient equation and your "auxiliary equation" doesn't make sense.
  5. Dec 22, 2009 #4


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    You mean u= l(d^2i/dt^2)+ (1/c)i+ r(di/dt)

    No, the auxiliary equation would be [itex]1,4r^2+ 1000 di/dt+ 3.2= 0[/itex]. You are mixing up L and C.

    What is u? A constant? If so, try a solution of the form i= A, a constant. What would A have to be to satisfy that equation?
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