Home
Class 12
MATHS
The order and degree of the differential...

The order and degree of the differential equation `(d^(4)y)/(dx^(4))=y+((dy)/(dx))^(4)` are

A

2, 4

B

4, 1

C

4, 2

D

2, 2

Text Solution

AI Generated Solution

The correct Answer is:
To determine the order and degree of the given differential equation \[ \frac{d^4y}{dx^4} = y + \left(\frac{dy}{dx}\right)^4, \] we will follow these steps: ### Step 1: Identify the highest derivative The first step is to identify the highest derivative present in the equation. In this case, we have: - \(\frac{d^4y}{dx^4}\) which is the fourth derivative of \(y\). - \(\frac{dy}{dx}\) which is the first derivative of \(y\). The highest derivative is \(\frac{d^4y}{dx^4}\), which indicates that the order of the differential equation is 4. ### Step 2: Determine the order The order of a differential equation is defined as the highest order of derivative present in the equation. Since the highest derivative here is the fourth derivative, we conclude that: \[ \text{Order} = 4. \] ### Step 3: Identify the degree Next, we need to find the degree of the differential equation. The degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in derivatives. In our equation, we can see that: - The highest order derivative \(\frac{d^4y}{dx^4}\) appears to the power of 1. - The term \(\left(\frac{dy}{dx}\right)^4\) is not affecting the degree of the highest derivative since it is not in the same polynomial form as \(\frac{d^4y}{dx^4}\). Since the highest order derivative \(\frac{d^4y}{dx^4}\) is raised to the power of 1, we conclude that: \[ \text{Degree} = 1. \] ### Final Conclusion Thus, the order and degree of the given differential equation are: - **Order**: 4 - **Degree**: 1
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    ML KHANNA|Exercise Problem Set (1) (TRUE AND FALSE)|8 Videos

  • DIFFERENTIAL EQUATIONS

    ML KHANNA|Exercise Problem Set (1) (FILL IN THE BLANKS)|9 Videos

  • DETERMINANTS

    ML KHANNA|Exercise Self Assessment Test |19 Videos

  • DIFFERENTIATION

    ML KHANNA|Exercise MESCELLANEOUS EXERCISE|3 Videos

Similar Questions

Explore conceptually related problems

Order and degree of the differential equation (d^(4)y)/(dx^(4))=(1+((dy)/(dx))^(2))^(3) respectively are

Order and degree of the differential equation (d^(2)y)/(dx^(2))={y+((dy)/(dx))^(2)}^(1//4) are

The order and degree of the differential equation (d^(2)y)/(dx^(2))=root(3)(1-((dy)/(dx))^(4)) are respectively

The order and degree of the differential equation (d^(2)y)/(dx^(2))+((dy)/(dx))^(1//4)+x^(1//5)=0 respectively are

The order and degree of the differential equation (d^(2)y)/(dx^(2))+((dy)/(dx))^((1)/(3))=0 are respectively

The order and degree of the differential equation (d^(2)y)/(dx^(2))=(1+((dy)/(dx))^(2))^(3/2) are

The order and degree of the differential equation (d^(3)y)/(dx^(3))=root5(1+((dy)/(dx))) is :

The order and degree of the differential equation , (d^(3)y)/(dx^(3))+sqrt(((dy)/(dx))^(3)+y^(2))=0

The order and degree of the differential equation " ((d^(2)y)/(dx^(2))+((dy)/(dx))^(3))^((6)/(5))=6y is