1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solution of differential with initial conditions

  1. Feb 12, 2012 #1
    I think my book is giving me the wrong answer....The problem is to find solution of following:

    r'(t) = t2[itex]\hat{i}[/itex] + 5t[itex]\hat{j}[/itex] + [itex]\hat{k}[/itex]

    The initial condition is:
    r(1) = [itex]\hat{j}[/itex] + 2[itex]\hat{k}[/itex]

    My solution:

    r(t) = < (1/3)t3 + c1 , (5/2)t2 + c2 , t+c3 >

    r(1) = < 0 , 1 , 2 >
    r(1) = < (1/3)+c1 , (5/2)+c2 , 1+c3 >

    Therefore:
    < 0 , 1 , 2 > = < (1/3)+c1 , (5/2)+c2 , 1+c3 >

    Solving for the three c's yields:
    c1 = -(1/3)
    c2 = -1.5
    c3 = 1

    And so the solution with the initial conditions is:
    < (1/3)t3 - (1/3) , (5/2)t2 -1.5 , t+1 >

    My book gives the solution as:
    < (1/3)t3 , (5/2)t2 + 1 , t+2 >

    Who is right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 12, 2012 #2

    Mark44

    Staff: Mentor

    Your work looks fine to me. Possibly there is a typo in the book's solution, or maybe you are not working the same problem.

    In the future, you can check these problems very easily. When you have your solution, check that
    1) the initial condition is satisfied. For your problem, you're checking that r(1) = <0, 1, 2>, and
    2) your solution satisfies the differential equation. Here, you're checking that r'(t) = <t^2, 5t, 1>.
     
  4. Feb 12, 2012 #3
    thanks!
    yea i checked a thousand times if i am working the same problem as the book and i am.
    i think the book meant to give the initial condition at r(0) not r(1)

    this is like the third typo in this book so far..i cant believe i paid some 120$ for bunch of typos!!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook