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Help with two simple equations

  1. Jan 23, 2012 #1
    Hello, I have just started learning differential equations.
    I am stuck on solving these two by separating the variables and writing the general solution.
    Can someone please show me the procedure.

    1. dy/dx = 1/y

    2. xdy/dx = y

    Thanks kindly for any help.
     
  2. jcsd
  3. Jan 23, 2012 #2

    Simon Bridge

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    Think the dy and dx as functions of x and y respectively, so dy/dx is just an ordinary division. Separation of variables is just the same as algebra - you need to get all the terms with a y on one side of the equals sign and all the terms with an x on the other side.

    so for:
    dy/dx=x you multiply both sides by dx to get dy=x.dx

    then you just write an integration sign in front of each expression.
    ∫dy = ∫x.dx

    now you follow that procedure for your examples.
     
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