CBSE Important Questions Class 12 Maths Chapter 9

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.

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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

1. 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.

1. 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.

1. 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

1. dy/dx – y = 0

1. 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.