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anonymous

  • one year ago

Find the two values of k for which y(x) = e^(kx) is a solution of the differential equation y" - 4y' + 0y = 0

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  1. anonymous
    • one year ago
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    @pooja195

  2. anonymous
    • one year ago
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    @ganeshie8

  3. ChillOut
    • one year ago
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    All right, first we should have \(k²*e^{kx}-4ke^{kx}=0\)

  4. ChillOut
    • one year ago
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    which leads to \((k-4)*k*e^{kx}=0\)

  5. ChillOut
    • one year ago
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    Now you are able to finish it.

  6. anonymous
    • one year ago
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    Woah woah woah, diff eq's aren't my strong suit, I'm just getting started. could you walk me into getting the k^2 * e^(kz)-4ke^(kx) = 0?

  7. anonymous
    • one year ago
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    Oops, x, not z

  8. anonymous
    • one year ago
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    Is it just doing second derivative of the function, and the first derivative, then subbing into the form given?

  9. ChillOut
    • one year ago
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    All right. For differential equations you must know derivatives... The differential equation in question \((y''(x)-4y'(x)+0y=0\)) is a second order linear ordinary differential equation, y''(x) is the second derivative of y(x) and y'(x) is the first derivative.

  10. ChillOut
    • one year ago
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    All I did was the differentiation of the given solution. Afterwards I plugged the solution in the equation.

  11. anonymous
    • one year ago
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    So with this all plugged in now, I want to solve for x = 0? Or find k in terms of x?

  12. ChillOut
    • one year ago
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    No, you don't want to solve in terms of x. You want find a value for k in which the left-hand side is equal to the right-hand side. (This is stated in the beggining of the question).

  13. ChillOut
    • one year ago
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    The question doesn't asks for values x, and most likely will never ask, unless it is a boundary value problem or initial value problem.

  14. ChillOut
    • one year ago
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    values of x*

  15. anonymous
    • one year ago
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    So I just want values for k that will make \[ke ^{kx}(k-4)\] equal to zero? I'm sorry if I'm still a little confused

  16. ChillOut
    • one year ago
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    Yes, you are right.

  17. anonymous
    • one year ago
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    0 and 4?

  18. ChillOut
    • one year ago
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    Yeah. Spot on!

  19. anonymous
    • one year ago
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    Wow, that was easier than I expected

  20. anonymous
    • one year ago
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    Thanks Chill!

  21. ChillOut
    • one year ago
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    When it gives you a solution, you will want to plug that solution and its derivatives in the ODE. That's how this kind of question is done.

  22. anonymous
    • one year ago
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    ODE being Order of Diff Eq's? Will the form given in this problem always be the same?

  23. anonymous
    • one year ago
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    Meaning y" - 4y' + 0y = 0

  24. ChillOut
    • one year ago
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    Nope, Ordinary Differential Equation. We have the PDEs too, but that's later for you :P

  25. anonymous
    • one year ago
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    Can I ask one more question on this topic? I've done out the work but can't see where Differential Equations fit in

  26. ChillOut
    • one year ago
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    Sure. Ask away.

  27. anonymous
    • one year ago
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    The solution of a certain differential equation is of the form \[y(t)=ae ^{2t} + be ^{3t}\] where a and b are constants. The solution has initial conditions y(0) = 4 and y'(0) = 3. Find the solution bu using the initial conditions to get linear equations for a and b

  28. ChillOut
    • one year ago
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    Show me what you have done until now.

  29. anonymous
    • one year ago
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    I did it out, and I'm pretty sure that a = -1 and b = 5. I thought I was supposed to thenn just substitute those numbers in for a and b, and call it a day, but my homework program says that's wrong

  30. anonymous
    • one year ago
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    Here's what I did

  31. anonymous
    • one year ago
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    f(0)=4, so a+b should =4, and we can get a = 4-b

  32. anonymous
    • one year ago
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    Then I found the derivative, y'(t) = 2ae^(2t)+3be^(3t)

  33. anonymous
    • one year ago
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    Subbed in 0 and set it equal to 3, where I found that 3 = 8-b, so b = 5

  34. anonymous
    • one year ago
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    Then I went back and subbed the new b into a = 4-b to get a = -1

  35. anonymous
    • one year ago
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    Submitted as an answer -1e^(2t)+5e^(3t) but webwork said it was wrong

  36. ChillOut
    • one year ago
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    Well, I dunno how they accept the answers, so in this one I can't help you :(

  37. ChillOut
    • one year ago
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    But yes, you did it right.

  38. anonymous
    • one year ago
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    Huh... Okay, well thanks again man!

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