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Third-order non-homogeneous linear ODE

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  • 28-12-2015 5:12pm
    #1
    SByrne55
    Registered Users Posts: 5 ✭


    xy''' + 2y'' = x
    y(General solution)=Yc + Yp
    Yc= c1(e^x) + c2
    Find the particular solution i.e Yp
    I've tried finding a series solution and using variation of parameters in conjunction with using the Wronskian (W(x)) in the formula below, but I can't seem to solve it

    Yp= -Y1*(integral(Y2(x)*x/W(x))dx) + Y2*(integral(Y1(x)*x/W(x))dx)


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    #2
    ride-the-spiral
    Registered Users Posts: 1,263 ✭✭✭ride-the-spiral


    I think you might be overcomplicating it with the Wronskian approach (which I'm not too sure how to use myself.) Since the lowest derivative that appears is y'', you can let z=y'' and the problem breaks into a first order ODE to solve for z followed by a 2nd order to solve for y''.


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