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V and x separable?

  1. Feb 14, 2016 #1
    1. The problem statement, all variables and given/known data
    i am asked to form a differential equation using dy/dx = 1 + y + (x^2 ) + y(x^2) , but i gt stucked here , hw to proceed? as we can see , the V and x are not separable

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Feb 14, 2016 #2
    Hi hotjohn:

    You may have a typo. You say
    V and x are not separable​
    but the is no "V" in the equation.

  4. Feb 14, 2016 #3
    sorry , i mean y and x . How to continue ?
  5. Feb 14, 2016 #4
    Hi hotjohn:

    If you factor the 2nd equation in your attachment, and make a substitution for y in terms of a new variable, say z, you can get a separable equation involving z and x.

    Hope this helps.

  6. Feb 14, 2016 #5
    sorry , i didnt get you , can you explain further ?
  7. Feb 14, 2016 #6
    Hi hotjohn:

    dy/dx = (1+y) × (1+x2)
    y = z-1

  8. Feb 14, 2016 #7
    can you expalin why there is a need to sub y = z-1 ?? and how do u knw why should sub y = z-1 ? why cant be y = z-2 ? or others ?
  9. Feb 14, 2016 #8
    You don't have to sub if you don't want to. Once it's separated just solve it like you would any seperable equation.
  10. Feb 14, 2016 #9
    how to determine the value of number or new constant to be substituted into the original equation ?
  11. Feb 14, 2016 #10
    Remember, unless you are given initial conditions you will have an infinite amount of answers to most differential equations.
  12. Feb 15, 2016 #11
    can it be y = z-2 , y = z-3 and etc ??
  13. Feb 15, 2016 #12
  14. Feb 15, 2016 #13
    i found that if substituition of y=z-1 is not used , the whole equation become inseparable ...........

    how do we know that y must be replaced with y=z-1 ?
  15. Feb 15, 2016 #14
    Hi hotjohn:

    As I said previously, using y = z-1 is not a necessity, and not something that must be done. I thought that making that substitution might help you see the separability more easily.

    Can you complete the solution of the problem from
    dy/dx = (1+y) × (1+x2) ?​

    If so, you are done.

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