Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Soroban

Math Help - differential equation

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Glasgow
    Posts
    3

    differential equation

    hi guys,
    Im struggling with this question on differential equations: dy/dx = (1+siny)/cosy.
    I separated x and y, integrated and got to the point ln (1+siny)=x+const. but cant find any way to express this equation in the form y= something.
    can anyone help me please?
    thanks a lot for any help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,735
    Thanks
    642

    Re: differential equation

    Hello, vervas!

    \frac{dy}{dx} \:=\: \frac{1+\sin y}{\cos y}

    I got: . \ln(1+\sin y)\:=\:x+c

    But can't solve for y.

    We have: . \ln(1+\sin y) \:=\:x + c

    Exponentiate: . 1 + \sin y \:=\:e^{x+c} \:=\:e^x\cdot e^c \:=\:Ce^x

    . . . . \sin y \;=\;Ce^x-1 \quad\Rightarrow\quad y \;=\;\sin^{-1}\!\left(Ce^x-1\right)
    Thanks from vervas
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: differential equation

    Are you required to solve for y? Many first order differential equations are satisified by some f(x, y)= constant where y is NOT a function of x. Soroban's solution (using the principle arc cosine) gives one solution out of many. Adding multiples of 2\pi will give other solutions.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2013
    From
    Glasgow
    Posts
    3

    Re: differential equation

    thank you! I got it except this part: e^x*e^c = C* e^x, could you explain that please?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2013
    From
    Glasgow
    Posts
    3

    Re: differential equation

    to HallsofIvy
    well, the question says : find the general solution of following equations, so it seems like I am not required to express it in the form y = ... but I though its to most useful expression
    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. Partial differential equation-wave equation(2)
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 6th 2009, 08:54 AM
  4. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 11:39 AM
  5. Replies: 13
    Last Post: May 19th 2008, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum