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What is the number of arbitrary constant...

What is the number of arbitrary constant in the particular solution of differential equation of third order ?

A

0

B

1

C

2

D

3

Text Solution

AI Generated Solution

The correct Answer is:
To determine the number of arbitrary constants in the particular solution of a third-order differential equation, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Differential Equations**: A differential equation relates a function to its derivatives. The order of a differential equation is determined by the highest derivative present in the equation. 2. **Identifying the Order**: In this case, we are dealing with a third-order differential equation. This means that the highest derivative in the equation is the third derivative. 3. **General Solution of a Differential Equation**: The general solution of a differential equation of order \( n \) contains \( n \) arbitrary constants. This is because each integration introduces a constant. 4. **Applying to Third-Order**: For a third-order differential equation, when we integrate three times to find the general solution, we will introduce three arbitrary constants. 5. **Conclusion**: Therefore, the number of arbitrary constants in the particular solution of a third-order differential equation is 3. ### Final Answer: The number of arbitrary constants in the particular solution of a third-order differential equation is **3**. ---
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Knowledge Check

  • The number of arbitrary constants in the particular solution of differential equation of third order is

    A
    3
    B
    2
    C
    1
    D
    zero

  • The numbers of arbitrary constants in the particular solution of a differential equation of third order are :

    A
    3
    B
    2
    C
    1
    D
    0

  • 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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    The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4

    Assertion: The general solution of ( dy ) /( dx) + y =1 is y e^x = e ^(X)+C Reason: The number of arbitrary constant in the general solution of the differential equation is equal to the order of D.E.

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    Statement 1: Order of a differential equation represents the number of arbitrary constants in the general solution.Statement 2: Degree of a differential equation represents the number of family of curves.

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