In this question you are asked to write general form of certain equations. In or

Question

In this question you are asked to write general form of certain equations. In order to do that you need to choose notation to denote some arbitrary functions. I suggest you use P(t), Q(t), R(t), G(t), etc. The answer to the first one is given to help you get started. A. Write down the most general form of a first order linear non-homogeneous equation. Answer: Any first order linear non-homogeneous equation can be written as P(t)y' + Q(t)y = G(t) where G(t) is non-zero. If G(t) 0, it'd become first order linear homogeneous. B. Write down the most general form of a second order linear homogeneous equation. C. Write down the most general torm of a second order linear nonhomogeneous equation D. Write down the most general form of a third order linear nonhomogeneous equation

Explanation / Answer

A)The most general form of a first order linear non-homogeneous equation is P(t)y'+Q(t)y=R(t), where R(t) is not the identically zero function.

B) The most general form of a second order linear homogeneous equation is:

P(t)y''+Q(t)y'+R(t)y=0. Any second order linear homogeneous equation can be written in this form.

C) The most general form of a second order linear non-homogeneous equation is :

P(t)y''+Q(t)y'+R(t)y=S(t), where S(t) is not the identically zero function. Any second order linear non-homogeneous equation is of this form.

D) The most general form of a third order linear non-homogeneous equation is:

H(t)y'''+P(t)y''+Q(t)y'+R(t)y=S(t), where S(t) is not the identically zero function. Any third order linear non-homogeneous equation can be written in this form.

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