Results 1 to 4 of 4

Math Help - differential equation madness!

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    45

    differential equation madness!

    differential equation (dy/dx) = sin(y - x) is given show that if a new variable is defined by y = z^(1-n) then the equation (dz/dx) + p(x)z = q(x)z^n becomes a linear differential equation in y(x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    Then just do it.

    We have \frac{dz}{dx}\cdot \frac{1}{{{z}^{n}}}+\frac{p(x)}{{{z}^{n-1}}}=q(x) which is a Bernoulli ODE so put y=\frac1{z^{n-1}}=z^{1-n} (and note that this is the suggested substitution) and you'll turn that ODE into a linear one.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    45
    i was given this and not taught Bernoulli's method, i read about it just now, it makes sense now, but isn't there another easier way to figure this out assuming you have no knowledge of bernoulli's equations and integrals (whatever there called)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    Actually, in your problem was never told about Bernoulli's ODE; by following the substitution suggested, you must conclude that you'll get a linear ODE.

    I just said that it is a Bernoulli's ODE since that's the way it's called, but nothing else.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  2. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  3. Pulley and Tension Madness! (Load weight)
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 29th 2010, 02:25 AM
  4. Square root madness!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 26th 2009, 02:17 AM
  5. Integral: have madness, need method
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 7th 2009, 12:52 PM

Search Tags


/mathhelpforum @mathhelpforum