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Homework Help: Homework help

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

    1) Solve the differential equation

    Here is what I did:

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

    Here is what I did:



    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:


    and since



    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.

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

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

    Now integrate both sides.
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