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If m, n are order and degree of differen...

If m, n are order and degree of differential equation `y(dy)/(dx) + x^(3)((d^(2)y)/(dx^(2)))-xy = cos x` then

A

`m lt n`

B

m= n

C

`m gt n`

D

m-n = 3

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the order and degree of the given differential equation: \[ y \frac{dy}{dx} + x^3 \frac{d^2y}{dx^2} - xy = \cos x \] ### Step 1: Identify the highest order derivative The highest order derivative in the equation is \( \frac{d^2y}{dx^2} \). This indicates that the order of the differential equation is 2. ### Step 2: Determine the degree of the highest order derivative 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 this case, the highest order derivative \( \frac{d^2y}{dx^2} \) appears to the first power (i.e., it is not raised to any power other than 1). ### Step 3: Conclusion on order and degree From the analysis: - The order \( m \) of the differential equation is 2. - The degree \( n \) of the differential equation is 1. ### Final Result Thus, we have: - \( m = 2 \) - \( n = 1 \)
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Knowledge Check

  • The order and degree of differential equation: [1+((dy)/(dx))^(2)]=(d^(2)y)/(dx^(2)"are"

    A
    `2,(3)/(2)`
    B
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    B
    3,1
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    3,3
    D
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  • The order and degree of the differential equation (d^(2)y)/(dx^(2))=sqrt(1+((dy)/(dx))^(3)) , is

    A
    2,2
    B
    1,2
    C
    2,3
    D
    2,1

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