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ODE Problems

  1. Sep 9, 2009 #1

    A little introduction, my name is Alfonso, I'm a Physics major. I'm orginally from Mexico but I've been living in the States for about half my life. I'm beginning my third year of college at Texas Tech and am thoroughly enjoying my time here! I'm actually a bit behind on my classes because I was transferred late and missed two days of school. This actually led me to my debut here! (I don't know if that's a good thing yet) My professor kindly lended my $200 to purchase my Differential Equations book for ODE about half an hour ago. I've been struggling with this homework. So far I've shot three problems down but the rest of these (posted) are perplexing me. I was wondering if I could get some help? I look forward to contributing in the future! =D

    Problem #1
    Find the position http://webwork.math.ttu.edu/wwtmp/equations/aa/8727e53c828c4d86d5c60edbbf40ec1.png [Broken] of a moving particle with the given acceleration http://webwork.math.ttu.edu/wwtmp/equations/72/ac5d7e539f91d520f21d357bcf7e5e1.png [Broken], initial position http://webwork.math.ttu.edu/wwtmp/equations/ad/4899084e580a79133cf44eded9da561.png [Broken], and initial velocity http://webwork.math.ttu.edu/wwtmp/equations/0c/e42c79e45f5ab6a87cc4927b0ea3831.png [Broken]

    http://webwork.math.ttu.edu/wwtmp/equations/57/449da94945160e834abdaeaa07482b1.png [Broken].

    http://webwork.math.ttu.edu/wwtmp/equations/ed/055d3c2feee89d38e7a107e1f9295f1.png [Broken] ____

    Problem #2
    The general solution to http://webwork.math.ttu.edu/wwtmp/equations/0d/9aa457ffd2e5fd57019eb3dc9509db1.png [Broken] can be written in the form http://webwork.math.ttu.edu/wwtmp/equations/ee/e1587a9f2447ef060c9bcee0b50a3d1.png [Broken] where [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8f/ef7df1811915931ddec43c23ba91971.png [Broken] [Broken] is an arbitrary constant.

    [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8b/0b3b5b8f0003a2d7dd6750d2846db31.png [Broken] [Broken] ____ For this problem I keep getting ln |y| = 3 ln |2+x| +C Is this correct? Am I missing a step?

    Problem #4
    The solution to http://webwork.math.ttu.edu/wwtmp/equations/07/c2f63eb85fff45d596ccdb23d6a5f51.png [Broken] with http://webwork.math.ttu.edu/wwtmp/equations/7d/c4d9a585631fc66949ef3e54457c291.png [Broken] is

    [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/ea/e6cfcd8bc239c880ec11f7a55587d41.png [Broken] [Broken] ____ For this problem I get y = square root of 2e^x +C is this correct?

    Problem #5
    The general solution of the first order linear equation http://webwork.math.ttu.edu/wwtmp/equations/ba/acc22b431c3dd54785050bbe4867de1.png [Broken] can be written as http://webwork.math.ttu.edu/wwtmp/equations/b7/275c75cc14d44935210377b1fba0731.png [Broken] where [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8f/ef7df1811915931ddec43c23ba91971.png [Broken] [Broken] is an arbitrary constant.

    [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8b/0b3b5b8f0003a2d7dd6750d2846db31.png [Broken] [Broken] ____
    Problem #6
    Solve the first order linear Initial value problem http://webwork.math.ttu.edu/wwtmp/equations/e9/eeb16dc4391cbd863fb98e7663f5111.png [Broken] with http://webwork.math.ttu.edu/wwtmp/equations/9f/d213edbcefb8312bf794d53d179c6b1.png [Broken].

    [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/ea/e6cfcd8bc239c880ec11f7a55587d41.png [Broken] [Broken] ____
    Problem #7
    Solve the first order linear Initial value problem http://webwork.math.ttu.edu/wwtmp/equations/79/578d76f7f8c2e0e712da65fb7c14381.png [Broken] with http://webwork.math.ttu.edu/wwtmp/equations/02/802f8b8b73ddcb133bd57d177493b11.png [Broken].

    [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/ea/e6cfcd8bc239c880ec11f7a55587d41.png [Broken] [Broken] ____

    Problem #8
    Solve the equation http://webwork.math.ttu.edu/wwtmp/equations/ea/d19b5c803d270b9885f88e186529bd1.png [Broken] by first setting http://webwork.math.ttu.edu/wwtmp/equations/5a/aba0fdb4dd187e8f983082d943229b1.png [Broken] to obtain a first order equation for [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/a7/34522e64f905980d2440692bdd1a1a1.png [Broken] [Broken]. After you solve for [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/a7/34522e64f905980d2440692bdd1a1a1.png [Broken] [Broken] recall that http://webwork.math.ttu.edu/wwtmp/equations/fc/8dfa85b8f83a506b31b726dbff5c001.png [Broken] and solve the resulting pure time equation for http://webwork.math.ttu.edu/wwtmp/equations/85/067ce783e2f89ced535d722b824af51.png [Broken].

    The solution can be written as http://webwork.math.ttu.edu/wwtmp/equations/be/2ae53f79b69e6792e63a0850709f691.png [Broken] where http://webwork.math.ttu.edu/wwtmp/equations/4c/9829f8d94c26e0c1df882bc622fafd1.png [Broken] and http://webwork.math.ttu.edu/wwtmp/equations/b8/f60b6af1267d2e64128ce6f0c84c8c1.png [Broken] are arbitrary constants.

    [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8b/0b3b5b8f0003a2d7dd6750d2846db31.png [Broken] [Broken] ____
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 9, 2009 #2


    User Avatar
    Homework Helper

    For 1) v= ∫ a(t) dt and s=∫v(t)dt

    2) write your constant C as lnC instead and use nlogab=logab[n.

    4) Your general solution is correct but you were given that y(0)=1, so you need to use this to find a particular solution.

    5) Read http://en.wikipedia.org/wiki/Integrating_factor" [Broken]

    6,7) Same as #5

    8)If v=y' then what is y'' equal to (in terms of v)? Now put those into the ODE and you'll get a first order equation that can be easily solved.
    Last edited by a moderator: May 4, 2017
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