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Math Help - Differentiation help to find particular solution to initial value problem

  1. #1
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    Differentiation help to find particular solution to initial value problem

    Hi All

    I need to find a particular solution to initial value problem but I'm stuck.

    The problem is (attachment 666)

    I have found the general solution to be the following (attachment 777) but now I'm stuck. Do I need to differentiate this and if so, how would I do this for the terms with e^x.?
    Attached Thumbnails Attached Thumbnails Differentiation help to find particular solution to initial value problem-666.gif   Differentiation help to find particular solution to initial value problem-777.gif  
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  2. #2
    Senior Member Peritus's Avatar
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    you would do this using the product rule.
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  3. #3
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    does that mean that if i differentiate I will get the particular solution to the initial value problem?
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  4. #4
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    Quote Originally Posted by moolimanj View Post
    does that mean that if i differentiate I will get the particular solution to the initial value problem?
    No.

    You differentiate to get y'(x). You want y'(x) in order to use the boundary condition y'(0) = 3. You substitute x = 0 into the derivative and put the result equal to 3. That gives you a linear equation in C and D.

    You then use the boundary condition y(0) = -2. You substitute x = 0 into y and put the result equal to -2. That gives you a linear equation in C and D.

    Now solve the two linear equations simultameously to get the value of C and D.
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