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Math Help - ODE help

  1. #1
    tak
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    ODE help

    Code:
    
    
    
    
    
    
    (3x^2y-y^3)dx-(3xy^2-x^3)dy=0
    
    Please help solve the above


    <br />
d^2y/dx^2 -4dy/dx +3y = e^3e^x<br />

    Please solve both
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  2. #2
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    First one looks exact to me (divide out the dx). Then use the procedure involving potential functions for exact ODEs to find the solution. second is a linear non-homogeneous equation, so your general solution will be the general solution of the associated homogeneous equation plus any particular solution of the non-homogeneous equation. Since you have constant coefficients, you should use the method of undetermined coefficients.

    What have you already tried?
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  3. #3
    tak
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    trying out

    I got  xy^3 - x^3y -2/x^2 =a where a is a constant
    I use dz=partial z/partial x dx + partial z/ partial y dy method
    dunno correct or not

    by the way what is the definition of homogenous in layman terms thanks
    As for the second Q i got y= C1e^3x +C2e^x
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  4. #4
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    Quote Originally Posted by tak View Post
    I got  xy^3 - x^3y -2/x^2 =a where a is a constant
    I use dz=partial z/partial x dx + partial z/ partial y dy method
    dunno correct or not

    by the way what is the definition of homogenous in layman terms thanks
    As for the second Q i got y= C1e^3x +C2e^x
    The homogeneous solution is just what you get if the right side, typically written as f(x) is zero. It is independent of the right side of the fuction, or the inhomogeneous part. In other words, you will get the same homogeneous solution, no matter what f(x) is equal to.

    Edit...It might help to know the standard form for a Second Order ODE is Ay''+By'+Cy=f(x)

    Edit 2...This answer is correct so far, but you have only solved for the homogeneous solution. You need to set up, using the method of undetermined coefficients, a solution to the inhomogeneous part. It will be of the form: Ate^x because you need a solution linearly independent of the solutions you have already gotten.
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  5. #5
    tak
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    constant zero

    I found my c3 to be zero; the general solution is just the complementry solution. correct?
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  6. #6
    tak
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    answer correct?

    y=C1e^(3x) +C2xe^(3x) +0.5x^(3x)
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