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Linearizing a Non Linear Differential Eq

  1. Jun 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Use a suitable substitution to transform the nonlinear DE (dy)/(dx)+y=y² into a linear equation in the new variable z.
    and
    without solving the DE, justify the possible methods that can be used to solve the DE found in first part.

    2. Relevant equations

    I have no idea what to do in order to solve this.


    3. The attempt at a solution

    dy/dx=y2 -y
    dy/dx= y(y-1)

    ∫dy/y=∫(y-1)dx

    ln(y)=y-1??

    eln(y)=e(y-1)

    y= ey-1


    I don't think this is write, but this is what I have... can someone help?
     
  2. jcsd
  3. Jun 13, 2013 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Did you not understand the problem? Surely you saw the "without solving the DE" part?

    (And "[itex]\int y-1 dx[/itex]", where y is an unknown function of x, is certainly not "y- 1". If you do not know y as a function of x, you cannot integrate with respect to x. If you wanted to solve the equation, you should instead completely separate "x" and "y":
    [tex]\int \frac{dy}{y(y-1)}= \int dx[/tex]
    using "partial fractions" on the left.)
     
  4. Jun 13, 2013 #3
    Sorry I might have written the questions wrong, first part is separate from the second part.
    The questions below are the right ones

    3a.Use a suitable substitution to transform the nonlinear DE (dy)/(dx)+y=y² into a linear equation in the new variable z.
    3b.without solving the DE, justify the possible methods that can be used to solve the DE found in 3a.
     
  5. Jun 13, 2013 #4

    CAF123

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    Gold Member

  6. Jun 13, 2013 #5
    You are a life saver! Thankyou so much!!

    :-)
     
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