Results 1 to 6 of 6

Math Help - DE question

  1. #1
    Junior Member
    Joined
    Jun 2007
    Posts
    27

    DE question

    im doing my DE HW and i dont understand how the book came out with an answer.. This is separable variables with an initial value.

    (dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1

    the answer is: y= sin ((1/2)x^2+c)

    and i have no idea where the sin came from...i know im probaly missing a rule somewhere, thanks for any help to get the jucices going!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by neven87 View Post
    im doing my DE HW and i dont understand how the book came out with an answer.. This is separable variables with an initial value.

    (dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1

    the answer is: y= sin ((1/2)x^2+c)

    and i have no idea where the sin came from...i know im probaly missing a rule somewhere, thanks for any help to get the jucices going!
    be sure you don't have a typo here, or that you are looking at the right question. because as the question is stated, your answer should be of the form x = f(t) not y = f(x)

    the answer i got is x = \tan \left( 4t - \frac {3 \pi}{4} \right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    534
    Thanks
    8
    And what's that c in the answer?
    Thought it was an IVP...


    I get the same answer as jhevon.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by neven87 View Post
    (dx/dt) = 4(x^2+1) the intial value is: x((pi)/4)=1
    \frac{1}{1+x^2} \cdot x' = 4

    \int \frac{1}{1+x^2} x' \ dt = \int 4 dt

    \tan^{-1} x = 4t+C

    x = \tan (4t+C)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jun 2007
    Posts
    27
    It was a misprint the answer is x= tan(4t-3/4(pi))
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jun 2007
    Posts
    27
    AH! missed the inverse tangent...thanks!
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum