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Second Order ODE

  1. Jan 7, 2012 #1
    Hi. I am new to differential equations. This is probably pretty easy but I don't quite understand how to do it yet.

    The equation is y^4 -3y'' -4y = 0.

    I can figure out what class of equation it is. I can write it in the form y'' = F(y), but I am not really sure how to solve it.
     
  2. jcsd
  3. Jan 7, 2012 #2
    Actually I think the problem is y'''' - 3y'' -4y. But I am still not sure what to do.
     
  4. Jan 8, 2012 #3
    Sure it is y'''' - 3y'' -4y = 0 because dasy to solve.
    Solving y^4 - 3y'' -4y =0 is possible, but hard. It involves elliptic integral.
     
  5. Jan 11, 2012 #4
    This is ODE with constant coefficients..

    Suppose that the solution is y=e^rx, than solve it!

    i find that r=2, r=-2, r=i, r=-i

    which means that

    complementary solution of eqn is y=c_1*e^2x + c_2*e^-2x + c_3(sinx) + c_4(cosx)
     
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