1. Not finding help here? Sign up for a free 30min 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!

Homework help

  1. Jan 27, 2006 #1
    I need someone to look over my work if possible

    1) Solve the differential equation
    xdy=(5y+x+1)dx

    Here is what I did:
    x=(5y+x+1)dx/dy
    [tex]x=5xy+\frac{x^2}{2}+x[/tex]
    [tex]0=5xy+\frac{x^2}{2}[/tex]
    [tex]\frac{-x^2}{2}=5xy[/tex]
    [tex]y=\frac{-x}{10}[/tex]

    2) Solve: [tex]y(x^2-1)dx+x(x^2+1)dy=0[/tex]

    Here is what I did:

    [tex]x^2ydx-ydx+x^3dy+xdy=0[/tex]

    [tex]\frac{xdy-ydx}{x^2}+ydx+xdy=0[/tex]

    [tex]d(\frac{y}{x})+d(xy)=0[/tex]
    This is where I am stuck at. I need to have something multiply the first differential that will yield something in the form of [tex]\frac{y}{x}[/tex] and also have the same thing multiply the second differential and will yield something in the form of xy.

    3) Find a differential equation with the solution [tex]y=c_1sin(2x+c_2)[/tex]

    Here is what I did:

    [tex]y'=2c_1cos(2x+c_2)[/tex]

    and since
    [tex]c_1=\frac{y}{sin(2x+c_2)}[/tex]

    [tex]y'=\frac{2ycos(2x+c_2)}{sin(2x+c_2}[/tex]

    [tex]y'=2ycot(2x+c_2)[/tex]

    I'm not sure what to do after this. I know I need to somehow get rid of the [tex]c_2[/tex] constant, but I don't know how to do this.
     
  2. jcsd
  3. Jan 27, 2006 #2
    In the second one just get all of the x and dx terms on one side and all of the y and dy terms on the other. That should only take one step.

    [tex]
    y\left( {x^2 - 1} \right)dx + x\left( {x^2 + 1} \right)dy = 0
    [/tex]

    [tex]
    \Rightarrow \left( {\frac{{x^2 - 1}}{{x^2 + 1}}} \right)dx = - \frac{1}{y}dy
    [/tex]

    Now integrate both sides.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Homework help
  1. Homework Help (Replies: 4)

  2. Homework help (Replies: 2)

  3. Homework Help! (Replies: 4)

Loading...