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

Answer 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.