Chegg Guided Solutions for Elementary Differential Equations With Boundary Value Problems 2nd Edition: Chapter 2.10

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  • Step 1 of 5

    (a) Consider the initial value problem

    Euler method iteration formula is

    , where


    Therefore, the iterative formula becomes

    At the initial condition point that is,

    If we compare the given initial condition with . we get

    Therefore, the values are

  • Step 2 of 5

    (b) Using a step size of need to calculate , and . So if we plug h into the iteration formula in equation (1), we get

    With this, we can start to calculate .

    So, .

    Now we can calculate .

    So, .

    Finally, we calculate .

    Therefore, .

  • Step 3 of 5

    (c) Now we need to solve the initial value problem analytically. For , we have a separable differential equation, so we can calculate anti-derivatives of both sides to get the solution.

    So the general solution is .

  • Step 4 of 5

    Now we apply the initial condition and find the value for C.

    Therefore, and the solution is .
  • Step 5 of 5

    (d) Now we need to calculate the errors for the first three terms.


    First we calculate .

    Recall from part (b) that and .

    So .

    Now for , recall that and .

    So .

    Finally, we calculate with and .

    Therefore, .

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