Important Questions for CBSE Class 12 Maths Chapter 9-Differential Equations 2023-24

Important Questions for CBSE Class 12 Maths Chapter 9 – Differential Equations

Students can prepare for the CBSE Board exams with Extramarks’ Important Questions For Class 12 Maths Chapter 9 Differential Equations. Subject matter experts have prepared each and every question. Students should practise these crucial questions in addition to studying and working through the NCERT Book’s Differential Equation problems.

Numerous formulas and techniques are provided in Class 12 Maths Chapter 9 Important Questions for the solution of differential equations. To review all the chapters and perform well on the CBSE final exam, students can read through all the relevant questions for all the chapters of Maths for Class 12 here.

Get Access to CBSE Class 12 Maths Important Questions for the Academic Year 2023-24

You can also find CBSE Class 12 Maths Important Questions Chapter-by-Chapter Important Questions here:

CBSE Class 12 Maths Important Questions
Sr No	Chapter No	Chapter Name
1	Chapter 1	Relations and Functions
2	Chapter 2	Inverse Trigonometric Functions
3	Chapter 3	Matrices
4	Chapter 4	Determinants
5	Chapter 5	Continuity and Differentiability
6	Chapter 6	Application of Derivatives
7	Chapter 7	Integrals
8	Chapter 8	Application of Integrals
9	Chapter 9	Differential Equations
10	Chapter 10	Vector Algebra
11	Chapter 11	Three Dimensional Geometry
12	Chapter 12	Linear Programming
13	Chapter 13	Probability

Study Important Question for Class 12 Maths Chapter 9 – Differential Equations

These are examples of long answer questions. for further reference, please click on the link provided

Determine the order and degree (if defined) of the differential equation (y′′′)2 + (y″)3 + (y′)4 + y5 = 0

Solution: Given the differential equation is (y′′′)2 + (y″)3 + (y′)4 + y5 = 0

The highest-order derivative present in the differential equation is y′′′.

Therefore, its order is 3.

The given differential equation is a polynomial equation in y′′′, y′′, and y′.

The highest power raised to y′′′ is 2.

Hence, its degree is 2.

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

(A) 0 (B) 2 (C) 3 (D) 4

Solution: We know that the number of constants in the general solution of a differential equation of order n is equal to its order.

Therefore, the number of constants in the general equation of the fourth-order differential equation is four.

Hence, the correct answer is D.

Note: The number of constants in the general solution of a differential equation of order n is equal to zero.

Find the differential equation of the family of lines through the origin.

Solution: Let y = mx be the family of lines through the origin.

Therefore, dy/dx = m

Eliminating m (substituting m = y/x)

y = (dy/dx). x

or

dy/dx – y = 0

Form the differential equation representing the family of curves y = a sin (x + b), where a, and b are arbitrary constants.

Solution: Given,

y = a sin (x + b) … (1)

Differentiating both sides of equation (1) with respect to x,

dy/dx = a cos (x + b) … (2)

Differentiating again on both sides with respect to x,

d2y/dx2 = – a sin (x + b) … (3)

Eliminating a and b from equations (1), (2) and (3),

d2y/ dx2 + y = 0 … (4)

The above equation is free from the arbitrary constants a and b.

This is the required differential equation.

Q1.

$\begin{array}{l} Form a differential equation representing the family \\ of curves given by \frac{x}{a} + \frac{y}{b} = 1 . \end{array}$

Opt.

$\begin{array}{l} \frac{x}{a} + \frac{y}{b} = 1 \\ Differentiating both sides w . r . t . x, we get \\ \frac{1}{a} + \frac{1}{b} \frac{dy}{dx} = 0 \\ Againg, differentiating both sides w . \end{array}$

Ans.

$\begin{array}{l} \frac{x}{a} + \frac{y}{b} = 1 \\ Differentiating both sides w . r . t . x, we get \\ \frac{1}{a} + \frac{1}{b} \frac{dy}{dx} = 0 \\ Againg, differentiating both sides w . r . t . x, we get \\ \frac{1}{b} \frac{d^{2} y}{{dx}^{2}} = 0 \\ \frac{d^{2} y}{{dx}^{2}} = 0 y ‘ ‘ = 0 \\ Hence, the required differential equation is y = 0. \end{array}$

Q2.

$\begin{array}{l} Find the particular solution of the differential equation \\ \log (\frac{dy}{dx}) = 3 x + 4 y at (0) = 0 . \end{array}$

Opt.

$\begin{array}{l} \log (\frac{dy}{dx}) = 3 x + 4 y \frac{dy}{dx} = e^{3 x + 4 y} \\ \frac{dy}{dx} = e^{3 x} e^{4 y} \\ \frac{dy}{} \end{array}$

Ans.

$\begin{array}{l} \log (\frac{dy}{dx}) = 3 x + 4 y \frac{dy}{dx} = e^{3 x + 4 y} \\ \frac{dy}{dx} = e^{3 x} e^{4 y} \\ \frac{dy}{e^{4 y}} = e^{3 x} dx \\ Integrating both sides \\ « \frac{dy}{e^{4 y}} = « e^{3 x} dx \\ « e^{’ 4 y} dy = « e^{3 x} dx \\ \frac{e^{’ 4 y}}{’ 4} = \frac{e^{3 x}}{3} + c \\ Now at x = 0 and y = 0 \\ \frac{1}{’ 4} = \frac{1}{3} + c \\ ’ \frac{1}{3} ’ \frac{1}{4} = c \end{array}$

Q3.

$Solve: \frac{dy}{dx} = \frac{y}{x} e^{\frac{y}{x}}$

Opt.

$\begin{array}{l} \frac{dy}{dx} = \frac{y}{x} e^{\frac{y}{x}} \\ Let \frac{y}{x} = v \\ \frac{dy}{dx} = v + x \frac{dv}{dx} \end{array}$ $\begin{array}{l} \end{array}$

Ans.

$\begin{array}{l} \frac{dy}{dx} = \frac{y}{x} e^{\frac{y}{x}} \\ Let \frac{y}{x} = v \\ \frac{dy}{dx} = v + x \frac{dv}{dx} \\ v + x \frac{dv}{dx} = v e^{v} \\ x \frac{dv}{dx} = e^{v} \\ \frac{dv}{e} = \frac{dx}{x} \\ e^{’ v} dv = \frac{dx}{x} \\ Integrating both sides \\ « e^{v} dv = « \frac{dx}{x} \\ e^{’ v} = \log |x| + c \\ e^{\frac{’ y}{x}} = \log |x| + c \end{array}$

Please register to view this section

CBSE Class 12 Maths Important Questions

Chapter 1- Relations and Functions

Chapter 2- Inverse Trigonometric Functions

Chapter 3- Matrices

Chapter 4- Determinants

Chapter 5- Continuity and Differentiability

Chapter 6- Application of Derivatives

Chapter 7- Integrals

Chapter 8- Application of Integrals

Chapter 10- Vector Algebra

Chapter 11- Three Dimensional Geometry

Chapter 12- Linear Programming

Chapter 13- Probability

FAQs (Frequently Asked Questions)

By practising solving these questions, you will be able to manage time efficiently and score better marks in the exams.

The step-by-step solutions framed for these questions will act as the guide and help you in utilising formulas to answer precisely.

CBSE Important Questions Class 12 Maths Chapter 9