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Math Help - Diff Equations

  1. #1
    Junior Member
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    Diff Equations

    is the following linear and if linear state if linear inhomogeneous, or linear homogenous


    L(U)=U_x+UU_y
    L(U)=Y^2CosxU_x + U_(yxy)

    I am confused do I first have to find L(u+v) and then L(CU)

    Then do I have this correct

    L(U)=U_x+xU_y
    L(u+v)=(U+V)_x+x(U+V)_Y
    =U+V_x + xU_y+xV_y
    = L(u) + L(v)
    L(CU)= (cu)_x +x(cu)_Y
    = cu_x + xcu_y
    = c( u_x + xu_y)
    = cL(u)
    Then this is linear right, do I have to do the same thing to the other two, then how do I tell if it is homogenous or inhomogenious?
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  2. #2
    Super Member Rebesques's Avatar
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    What you have done is correct.

    Neither of the two is linear or homogeneous. To see this, calculate L(cu) in either case. One ends up with an extra c and one cannot have a common factor of c.
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