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Degree of differential equation (d^(2)y)...

Degree of differential equation `(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)+y=0` is :

A

3

B

2

C

1

D

0

Text Solution

AI Generated Solution

The correct Answer is:
To find the degree of the given differential equation \[ \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + y = 0, \] we will follow these steps: ### Step 1: Identify the highest order derivative The highest order derivative in the equation is \(\frac{d^2y}{dx^2}\). ### Step 2: Determine the order of the differential equation The order of the differential equation is determined by the highest derivative present. Here, since \(\frac{d^2y}{dx^2}\) is the highest derivative, the order of the differential equation is 2. ### Step 3: Identify the degree of the differential equation The degree of a differential equation is defined as the power of the highest order derivative when the equation is a polynomial in derivatives. In our case, the highest derivative \(\frac{d^2y}{dx^2}\) appears to the power of 1 (since it is not raised to any power). ### Step 4: Conclusion Thus, the degree of the differential equation is 1. ### Final Answer: The degree of the differential equation is 1. ---
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Knowledge Check

  • Order of the differential equation : (d^(2)y)/(dx^(2))-((dy)/(dx))^(3)+3y=0 is :

    A
    3
    B
    2
    C
    0
    D
    1

  • The degree of the differential equation ((d^(2)y)/(dx^(2)))+((dy)/(dx))^(2)=x sin((d^(2)y)/(dx)) , is

    A
    1
    B
    2
    C
    3
    D
    none of these

  • The degree and order of the differential equation : 2(d^(2)y)/(dx^(2))-3(dy)/(dx)+y=0 is :

    A
    (2, 1)
    B
    (1, 2)
    C
    (2, 2)
    D
    Not defined

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