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Question on Linearity

  1. Oct 19, 2014 #1
    Hi , I have no problem to solve but just a bit of confusion on what determines the linearity of an ODE.

    Let's say the equation is (1 x^2) dy/dx + y = 0

    Is it linear ? I would incline to say yes because the dependent variable and its derivatives are not in a product with each other but the square on the x makes me doubt the linearity or does it not matter at all? If it was (1-y^2), it wouldn't be linear because the coefficient has the dependent variable in it.

    Thanks ,
    GT
     
  2. jcsd
  3. Oct 19, 2014 #2

    hilbert2

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    Science Advisor
    Gold Member

    An ODE is linear if the sum of any two solutions to it is also a solution.

    Suppose we have two functions, ##y_{1}## and ##y_{2}##, and they both satisfy the ODE:

    ##(1-x^{2})\frac{dy_{1}}{dx} + y_{1}=0##
    ##(1-x^{2})\frac{dy_{2}}{dx} + y_{2}=0##

    Can you show that ##y_{1}+y_{2}## also satisfies the ODE? If you can, then the eq is linear.
     
  4. Oct 20, 2014 #3
    Not helpful at all . Just had to say yes or no .
     
  5. Oct 20, 2014 #4
    give a man a fish...
     
  6. Dec 14, 2014 #5
    Do the work and you'll get your answer. This isn't a forum for babies, please read the rules.
     
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