Find transient terms in this general solution to a differential equation, if there are any y=(x+C)(x+2x−2)

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Find transient terms in this general solution to a differential equation, if there are any  y=(x+C)(x+2x−2)

unett · Accepted Answer

(x+C)(x+2x−2)=x2x−2+(2+C)xx−2+2Cx−2 Then take the limits of each of these three terms as x→∞ and see which(if any) approach 0. All three are rational expressions, so it is clear that only 2Cx−2 is transient term.

xleb123 · Accepted Answer

To find the transient terms in the general solution of the given differential equation, we first need to rewrite the equation in a more standard form. The given general solution is:y=(x+C)(x+2x−2)To simplify the expression, we can expand it:y=(x+C)(x+2)x−2Now, let&#039;s write the expression in a more suitable form for identifying the transient terms:y=x2+(C+2)x+2Cx−2The transient terms are the terms in the numerator that have a power of x greater than or equal to the power in the denominator. In this case, the highest power in the denominator is 1 (since it is linear in x). Therefore, we are interested in the terms with x raised to the power of 2 or higher.The numerator can be expressed as:x2+(C+2)x+2CThe terms x2 and Cx have powers of x greater than 1. Thus, these are the transient terms.Therefore, the transient terms in the general solution are x2 and Cx.

fudzisako · Accepted Answer

Answer:4(x+C)x−2Explanation:y=(x+C)(x+2x−2)To analyze the transient terms, we&#039;ll rewrite the expression inside the parentheses as:x+2x−2=(x−2)+4x−2=1+4x−2Now we can substitute this back into the original equation:y=(x+C)(1+4x−2)Expanding this expression, we get:y=x+C+4(x+C)x−2Now we can identify the transient terms. The transient terms are those that tend to zero as x goes to infinity. In this case, the term 4(x+C)x−2 tends to zero as x approaches infinity, since the numerator grows linearly while the denominator grows faster. Therefore, the transient terms in the general solution are:4(x+C)x−2

Find transient terms in this general solution to a differential equation, if there are any y=(x+C)(frac{x+2}{x-2})

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