Second order differential equations

Discussion in 'Differentiation and Integration' started by Didi, Aug 11, 2017.

  1. Didi

    Didi

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    Can someone help me with the following :
    d^2y/dx^2 + d^2z/dx^2 +d^2w/dx^2 = N(x)
    Where N = y + z + w
     
    Didi, Aug 11, 2017
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  2. Didi

    HallsofIvy

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    It looks like you have only one equation in three unknowns. Typically, in such a situation, the best you can do is solve for one unknown in terms of the other two.
     
    HallsofIvy, Nov 12, 2021
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  3. Didi

    HallsofIvy

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    In fact, with y+ z+ w= N, w= N- y- z so dw/dx= -dy/dx- dz/dx and d^2w/dx^2= -d^2y/dx^2- d^2z/dx^2 so d^2/dx^2+ d^2z/dx^2+ d^2w/dx^2= d^2y/dx^2+d^2z/dx^2- d^2y/dx^2- d^2z/dx^2= 0= y+ z+ w.

    Any functions, y(x), z(x), w(x) that satisfy w(x)= -y(x)- z(x) will satisfy both equations!
     
    HallsofIvy, Nov 15, 2021
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