Solve the following initial value third order differential equation by using differential operator. Show the all steps of derivation, beginn

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Solve the following initial value third order differential equation by using differential operator. Show the all steps of derivation, beginning with the general solution of ODE

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Eden 1 month 2021-08-12T10:30:12+00:00 1 Answer 0 views 0

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    2021-08-12T10:31:12+00:00

    Step-by-step explanation:

    Theorem The general solution of the ODE a(x) d2y dx2 + b(x) dy dx + c(x)y = f(x), is y = CF + PI, where CF is the general solution of homogenous form a(x) d2y dx2 + b(x) dy dx + c(x)y = 0, called the complementary function and PI is any solution of the full ODE, called a particular integral.

    Here is a step-by-step method for solving them:

    • Substitute y = uv, and. …
    • Factor the parts involving v.
    • Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
    • Solve using separation of variables to find u.
    • Substitute u back into the equation we got at step 2.

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