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The numbers of arbitrary constants in th...

The numbers of arbitrary constants in the general solution of a differential equation of fourth order are :

A

0

B

2

C

3

D

4

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To determine the number of arbitrary constants in the general solution of a differential equation of fourth order, we can follow these steps: ### Step 1: Understand the relationship between the order of the differential equation and the number of arbitrary constants. The order of a differential equation indicates the highest derivative present in the equation. For a differential equation of order \( n \), the general solution will contain \( n \) arbitrary constants. ### Step 2: Apply the relationship to the given order. In this case, we have a differential equation of order 4. Therefore, according to the relationship mentioned, the general solution will contain 4 arbitrary constants. ### Step 3: State the conclusion. Thus, the number of arbitrary constants in the general solution of a differential equation of fourth order is **4**. ### Final Answer: The number of arbitrary constants in the general solution of a differential equation of fourth order is **4**. ---
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