Question:
Consider the following differential equations which are obtained by successive differentiations. Choose the correct answer from the options given below.
Consider the following differential equations which are obtained by successive differentiations. Choose the correct answer from the options given below.
Show Hint
In successive differentiation, product rule changes the coefficients of \(y_{n+1}\) and \(y_{n+2}\). Always check signs carefully.
Updated On: May 19, 2026
- B and C only
- A and D only
- B and D only
- A and C only
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
When a differential equation is differentiated successively, the new relation contains higher derivatives such as \(y_{n+1}\) and \(y_{n+2}\).
Step 1: Use successive differentiation rule.
Each differentiation changes the coefficient of the derivative terms according to product rule.
Step 2: Check the signs and coefficients.
For equations of the form: \[ (1-x^2)y''-xy'+a^2y=0 \] successive differentiation gives terms involving: \[ (1-x^2)y_{n+2} \] \[ -(2n+1)xy_{n+1} \] and \[ (a^2-n^2)y_n \]
Step 3: Identify correct statements.
By comparing the coefficients and signs, statements A and C follow the correct successive differentiation form. \[ A \text{ and } C \text{ are correct} \] \[ \therefore \text{Correct Answer is (D)} \]
When a differential equation is differentiated successively, the new relation contains higher derivatives such as \(y_{n+1}\) and \(y_{n+2}\).
Step 1: Use successive differentiation rule.
Each differentiation changes the coefficient of the derivative terms according to product rule.
Step 2: Check the signs and coefficients.
For equations of the form: \[ (1-x^2)y''-xy'+a^2y=0 \] successive differentiation gives terms involving: \[ (1-x^2)y_{n+2} \] \[ -(2n+1)xy_{n+1} \] and \[ (a^2-n^2)y_n \]
Step 3: Identify correct statements.
By comparing the coefficients and signs, statements A and C follow the correct successive differentiation form. \[ A \text{ and } C \text{ are correct} \] \[ \therefore \text{Correct Answer is (D)} \]
Was this answer helpful?
0
0
Top CUET PG Geophysics Questions
- The shape of air film formed between the plano-convex lens and the glass slab in Newton’s ring experiment is
- Match List I with List II:Choose the correct answer from the options given below:
List I List II (A) The linear momentum of the system remains constant (IV) The net external force acting on a system of particles is zero (B) The angular momentum of the system remains constant (III) The external torque acting on a system of particles is zero (C) Inertial frame (I) The frames relative to which an unaccelerated body appears unaccelerated (D) Non-inertial frame (II) The frames relative to which an unaccelerated body appears accelerated - Match List I with List II:Choose the correct answer from the options given below:
LIST I LIST II A. Maxwell's First Equation I. Modified Ampere's Law B. Maxwell's Second Equation II. Faraday's Laws of Electromagnetic Induction C. Maxwell's Third Equation III. Gauss Law in Electrostatics D. Maxwell's Fourth Equation IV. Gauss Law in Magnetostatics - The efficiency of Carnot’s engine working between the steam point and the ice point is:
- Match List I with List II:Choose the correct answer from the options given below:
List I List II (A) (∂S/∂P)T (I) (∂P/∂T)V (B) (∂T/∂V)S (II) (∂V/∂S)P (C) (∂T/∂P)S (III) -(∂V/∂T)P (D) (∂S/∂V)T (IV) -(∂P/∂S)V
View More Questions
Top CUET PG Mathematics Questions
- The value of tan(i log 2 − i√3 / 2 + i√3) is
- The value of the integral $$ \oint_C \left[ (x^3 + xy) \, dx + (x^2 - y^3) \, dy \right] $$ where $C$ is the square formed by the lines $x = \pm 1$, $y = \pm 1$, is:
- The surface integral \[ \iint_S \mathbf{F} \cdot d\mathbf{S} \] where \( \mathbf{F} = x\hat{i} + y\hat{j} - z\hat{k} \) and \( S \) is the surface of the cylinder \( x^2 + y^2 = 4 \) bounded by the planes \( z = 0 \) and \( z = 4 \), equals:
- The value of curl (\(\text{grad } f\)), where \( f = x^2 - 4y^2 + 5z^2 \), is:
- Let \( a \) be the magnitude of the directional derivative of the function: \[\phi(x, y) = \frac{x}{x^2 + y^2}\] along a line making an angle of \( 45^\circ \) with the positive x-axis at the point \( (0, 2) \). Then, the value of \( 1/a^2 \) is:
View More Questions
Top CUET PG Questions
- Given below are two statements:
Statement I: For Plato the meaning of the word 'Justice' is basically a conception in the mind only.
Statement II: For Plato the meaning of the word 'Justice' is fixed, mind-independently
In the light of the above statements, choose the correct answer from the options given below: - What is the electron count of OS6CO182-?
- XeF4 hydrolysis gives A + B, HF, and Oxygen. Find A and B
- What is more basic in pyrol and pyridine?
- Hydrolysis of Al2C3, Be2?
View More Questions