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

Question

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

## Answers ( )

1. 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.