Question:
The order and degree of differential equation \( \frac{d^2y}{dx^2} = 1 - \left( \frac{d^3y}{dx^3} \right)^2 \) is :
The order and degree of differential equation \( \frac{d^2y}{dx^2} = 1 - \left( \frac{d^3y}{dx^3} \right)^2 \) is :
Show Hint
Always locate the highest derivative first to find the order. The degree belongs exclusively to that specific term's exponent, regardless of how high other lower-derivative powers are.
Updated On: Jul 6, 2026
- Order = 3, Degree = 3
- Order = 2, Degree = 2
- Order = 3, Degree = 2
- Order = 2, Degree = 1
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
• Order: The order of a differential equation is defined as the highest derivative order present anywhere inside the equation.
• Degree: The degree is the power of the highest order derivative term, provided the differential equation is written as a polynomial expression in terms of its derivatives.
Step 1: Determine the order. Look at the derivative components present in the given equation: \[ \frac{d^2y}{dx^2} \quad \text{(Second derivative)} \] \[ \frac{d^3y}{dx^3} \quad \text{(Third derivative)} \] The highest derivative order appearing in the expression is \( 3 \). Thus, Order = 3.
Step 2: Determine the degree. Identify the term containing this highest derivative, which is \( \left( \frac{d^3y}{dx^3} \right)^2 \). The exponent power of this term is \( 2 \). Since the entire equation is a polynomial in derivatives, the degree is simply this exponent. Thus, Degree = 2.
• Order: The order of a differential equation is defined as the highest derivative order present anywhere inside the equation.
• Degree: The degree is the power of the highest order derivative term, provided the differential equation is written as a polynomial expression in terms of its derivatives.
Step 1: Determine the order. Look at the derivative components present in the given equation: \[ \frac{d^2y}{dx^2} \quad \text{(Second derivative)} \] \[ \frac{d^3y}{dx^3} \quad \text{(Third derivative)} \] The highest derivative order appearing in the expression is \( 3 \). Thus, Order = 3.
Step 2: Determine the degree. Identify the term containing this highest derivative, which is \( \left( \frac{d^3y}{dx^3} \right)^2 \). The exponent power of this term is \( 2 \). Since the entire equation is a polynomial in derivatives, the degree is simply this exponent. Thus, Degree = 2.
Was this answer helpful?
0
0
Top CBSE CLASS XII Mathematics Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A committee of 11 members is to be formed from 8 males and 5 females. Let m denotes the number of ways of selecting committee having atleast 6 males and n denotes the number of ways of selecting atleast 3 females then
Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
- Relation R in the set A={1,2,3,4,5,6} defined as R={(x,y): y is divisible by x}.
- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
View More Questions
Top CBSE CLASS XII Differential Equations Questions
- If the rate of change of volume of a sphere is twice the rate of change of its radius, then the surface area of the sphere is:
- The general solution of the differential equation \( \frac{dy}{dx} = 2x \cdot e^{x^2 + y} \) is:
- If \( m' \) and \( n' \) are the degree and order respectively of the differential equation \( 1 + \left( \frac{dy}{dx} \right)^3 = \frac{d^2 y{dx^2} \), then the value of \( (m + n) \) is: }
For the curve \( \sqrt{x} + \sqrt{y} = 1 \), find the value of \( \frac{dy}{dx} \) at the point \( \left(\frac{1}{9}, \frac{1}{9}\right) \).
- Find the general solution of the differential equation \[ x^2 \frac{dy}{dx} = x^2 + xy + y^2 \] OR
View More Questions
Top CBSE CLASS XII Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is
- A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be
- A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is
- A circular disc is rotating about its own axis at uniform angular velocity \(\omega.\) The disc is subjected to uniform angular retardation by which its angular velocity is decreased to \(\frac {\omega}{2}\) during 120 rotations. The number of rotations further made by it before coming to rest is
View More Questions