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Prove the following statement:

  1. Apr 14, 2005 #1
    Q. If y = y1 (x) is a solution of dy/dx + p(x) y = r(x) and y = y2(x) is a solution of dy/dx + p(x) y = q(x), then y = y1(x) + y2(x) is a solution of

    dy/dx + p(x) y = q (x) + r(x).

    I know that the a Linear differential equation is of the form,

    dy/dx + p(x) y = q(x)

    Any thoughts on how to proceed with this one.

    Would appreciate, ideas.
     
  2. jcsd
  3. Apr 14, 2005 #2

    Hurkyl

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    Please read the guidelines for posting homework help questions.

    https://www.physicsforums.com/showthread.php?t=4825

    You must have had a thought on something to do, even if it is something as trivial, such as rewriting a statement in terms of a definition.
     
  4. Apr 14, 2005 #3

    HallsofIvy

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    HOW do you show that a given function IS a solution to a differential equation? Show us what you have done or what you DO understand about this.
     
  5. Apr 19, 2005 #4
    d(y1+y2)/dx+P(y1+y2)=(dy1/dx+py1)+(dy2/dx+py2)
    =q(x)+r(x)
    since q and r are solutions of those non homogeneous differential equations
     
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