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Solve the given differential equations or initial-value problems

  1. Aug 9, 2010 #1
    Hello guys,

    I have these two questions that I spent s much time to solve them but couldn't.


    solve the given differential equations or initial-value problems

    * dy/dx = x/t


    * dy/dt = 3 + 5y

    It's about SEPARABLE FIRST-ORDER DIFFERENTIAL equations.

    Thank you so much,
     
  2. jcsd
  3. Aug 11, 2010 #2
    first try to solve second eq. dy/dt -5y=3 is a linear differansial eq. , you will get t(y)
    and put t(y) in the first eq. like: t(y).dy=x.dx, integrate this, here is the solution.
     
  4. Aug 11, 2010 #3
    It looks like you have two completely separate question there?

    Is there a typo or something in the first equation?

    The second equation: it's separable! dy/(3 + 5y) = dt. If you can't solve that question, you haven't understood the material.
     
  5. Aug 11, 2010 #4

    HallsofIvy

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    Science Advisor

    Your first equation doesn't make sense. There shouldn't be an "x" in the equation if nothing else is said about "x". You probably mean dy/dx= y/t.

    These are called "separable" because you can separate y and t. In the first equation dy/dx= y/t becomes (1/y)dy/dt= t and now you can treat the derivative dy/dt as the ratio of differentials (dy)/(dt) so that (1/y)dy= t dt and integrate both sides, (1/y)dy with respect to y and t dt with respect to t.

    Similarly, dy/dt= 3+ 5y becomes dy/(3+ 5y)= dt in "differential form" and you can again integrate both sides.
     
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