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Math Help - systems of linear equations

  1. #1
    Junior Member
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    systems of linear equations

    Let x=x1(t), y=y1(t) and x=x2(t), y=y2(t) be any two solutions of the linear nonhomogenous equation

    x'=p11(t)x+p12(t)y+g1(t),
    y'=p21(t)x+p22(t)y+g2(t)

    Show that x=x1(t)-x2(t), y=y1(t)-y2(t) is a solution of the corresponding homogenous system.

    Thank you!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by morganfor View Post
    Let x=x1(t), y=y1(t) and x=x2(t), y=y2(t) be any two solutions of the linear nonhomogenous equation

    x'=p11(t)x+p12(t)y+g1(t),
    y'=p21(t)x+p22(t)y+g2(t)

    Show that x=x1(t)-x2(t), y=y1(t)-y2(t) is a solution of the corresponding homogenous system.

    Thank you!
    Substitute into the equations and show that (x1,y1) and (x2,y2) being solutions implies that (x1-x2,y1-y2) is also a solution.

    CB
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