Results 1 to 5 of 5

Math Help - Bizzare diffeq calculation problems

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    2

    Bizzare diffeq calculation problems

    I'm learning very basic diffeqs in another math class, and the type of problems were doing are first order separable differential equations, very basic stuff.

    I'm trying to use Mathematica/Wolfram Alpha to check my answers, but everytime, wolfram will output the incorrect answer and I will always have the correct answer and I can't figure out why

    For example:

    7\sqrt{xy}\frac{dy}{dx}=4

    I calculated y to be:
    y=(\frac{3}{14}8\sqrt{x}+C)^\frac{2}{3}

    When simplified, this matches the back of my book. Great. When I type the same problem for Wolfram Alpha to solve, I get back this:

    Input:
    Solve \frac{dy}{dx}=\frac{4}{7\sqrt{xy}}

    Output:
    y = \frac{3}{14}^\frac{2}{3} (8 \sqrt{x} + 7*C)^\frac{2}{3}

    Which is completely wrong. Could this be a bug in the CAS?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Cluuia09320 View Post
    I'm learning very basic diffeqs in another math class, and the type of problems were doing are first order separable differential equations, very basic stuff.

    I'm trying to use Mathematica/Wolfram Alpha to check my answers, but everytime, wolfram will output the incorrect answer and I will always have the correct answer and I can't figure out why

    For example:

    7\sqrt{xy}\frac{dy}{dx}=4

    I calculated y to be:
    y=(\frac{3}{14}8\sqrt{x}+C)^\frac{2}{3}

    When simplified, this matches the back of my book. Great. When I type the same problem for Wolfram Alpha to solve, I get back this:

    Input:
    Solve \frac{dy}{dx}=\frac{4}{7\sqrt{xy}}

    Output:
    y = \frac{3}{14}^\frac{2}{3} (8 \sqrt{x} + 7*C)^\frac{2}{3}

    Which is completely wrong. Could this be a bug in the CAS?
    Both answers are equivalent. One of your mistakes is in assuming that the C in your answer is the same as the C in Wolfram's answer:

    = \left(\frac{3}{14} \cdot 8 \sqrt{x} + \frac{3}{14} \cdot 7 \cdot C\right)^\frac{2}{3} =  \left(\frac{3}{14} \cdot 8 \sqrt{x} + B \right)^\frac{2}{3}

    where the B here is just as arbitrary as your C.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    2
    Quote Originally Posted by mr fantastic View Post
    Both answers are equivalent. One of your mistakes is in assuming that the C in your answer is the same as the C in Wolfram's answer:

    = \left(\frac{3}{14} \cdot 8 \sqrt{x} + \frac{3}{14} \cdot 7 \cdot C\right)^\frac{2}{3} =  \left(\frac{3}{14} \cdot 8 \sqrt{x} + B \right)^\frac{2}{3}

    where the B here is just as arbitrary as your C.
    But the answers can't be equivalent...

    If we let the constant = 4.5 in both equations and we let x = 7 in both equations and solve for y

    4.3381=(\frac{3}{14}8\sqrt{7}+4.5)^\frac{2}{3}
    5.0313= \frac{3}{14}^\frac{2}{3} (8 \sqrt{7} + 7*4.5)^\frac{2}{3}

    Both equations are not equal
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Cluuia09320 View Post
    But the answers can't be equivalent...

    If we let the constant = 4.5 in both equations and we let x = 7 in both equations and solve for y

    4.3381=(\frac{3}{14}8\sqrt{7}+4.5)^\frac{2}{3}
    5.0313= \frac{3}{14}^\frac{2}{3} (8 \sqrt{7} + 7*4.5)^\frac{2}{3}

    Both equations are not equal
    They aren't literally equal but they are both solutions. Differentiate both.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Cluuia09320 View Post
    But the answers can't be equivalent...

    If we let the constant = 4.5 in both equations and we let x = 7 in both equations and solve for y

    4.3381=(\frac{3}{14}8\sqrt{7}+4.5)^\frac{2}{3}
    5.0313= \frac{3}{14}^\frac{2}{3} (8 \sqrt{7} + 7*4.5)^\frac{2}{3}

    Both equations are not equal
    I say again: "One of your mistakes is in assuming that the C in your answer is the same as the C in Wolfram's answer."

    You continue to make that mistake by letting "the constant = 4.5 in both equations."

    In my previous reply I showed you why the answers were equivalent (equivalent does not mean equal, by the way).

    Calculate the arbitrary constant in each solution for the initial condition y = 1, x = 0 and you will discover that each gives the same rule for y (provided you do this correctly, of course).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. diffEQ using L, D, Ly, y(x)... not sure how to approach this
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: February 24th 2010, 08:06 PM
  2. Replies: 3
    Last Post: December 14th 2009, 08:25 PM
  3. Some simple DiffEQ problems.
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 18th 2009, 06:18 AM
  4. diffeq problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 27th 2009, 08:56 AM
  5. Some more diffeq help
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 26th 2009, 04:18 PM

Search Tags


/mathhelpforum @mathhelpforum