CBSE Class 12th Mathematics Chapter 9 - Differential Equations Important Questions with Answers

You should focus on solving CBSE Class 12th Mathematics Chapter 9: Differential Equations important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 9 questions, you will be solving exam-oriented questions only.

Never Miss an Exam Update

Prepare thoroughly with the most important questions of CBSE Class 12th Mathematics Chapter 9 - Differential Equations. You can first cover the CBSE Class 12th Mathematics syllabus to understand the key topics and then start solving the CBSE Class 12th Mathematics Chapter 9 - Differential Equations Important Question to get a better understanding of your preparation level. Start practicing now.

Are you feeling lost and unsure about what career path to take after completing 12th standard?

Say goodbye to confusion and hello to a bright future!

Was this article helpful?

0 Upvotes

0 Downvotes

Find the order and the degree of the differential equation. (Delhi 2019)
x²\(\frac{d^{2} y}{d x^{2}}=\left\{1+\left(\frac{d y}{d x}\right)^{2}\right\}^{4}\)

Question 2.

Write the order and degree of the differential equation. (Delhi 2019, 2013)
x³\(\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+x\left(\frac{d y}{d x}\right)^{4}\) = 0

Question 3.

Find the order and degree (if defined) of the differential equation. (All India 2019)
\(\frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}=2 x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right)\)

Question 4.

Find the differential equation representing the family of curves y = ae^2x + 5 constant. (All India 2019)

Question 5.

Form the differential equation representing the family of curves y = e^2x(a + bx), where ‘a’ and ‘b’ are arbitrary constants. (Delhi 2019)

Question 6.

Find the differential equation of the family of curves y = Ae^2x + Be^-2x, where A and B are arbitrary constants. (All India 2019)

Question 7.

Find the general solution of the differential equation \(\frac{d y}{d x}\) = e^x+y. (All India 2019)

Question 8.

Solve the differential equation
(x + 1)\(\frac{d y}{d x}\) = 2e^-y – 1; y(0) = 0 (Delhi 2019)

Question 9.

Solve the following differential equation. x dy – y dx = \(\sqrt{x^{2}+y^{2}}\) dx, given that y = 0 when x = 1. (Delhi 2019; All India 2011)

Question 10.

Solve the differential equation
(1 + x)² + 2xy – 4x² = 0, subject to the initial condition y(0) = 0. (Delhi 2019)

Question 1.

Solve the differential equation
\(\frac{d y}{d x}-\frac{2 x y}{1+x^{2}}\)y = 1 + x² (Delhi 2019)

Question 2.

Solve the following differential equation.
x \(\frac{d y}{d x}\) = y – x tan\(\left(\frac{y}{x}\right)\). (All IndIa 2019)

Question 3.

Solve the differential equation. (All India 2019)
\(\frac{d y}{d x}=-\left[\frac{x+y \cos x}{1+\sin x}\right]\)

Question 4.

Find the differential equation representing the family of curves y = ae^bx+5, where a and b are arbitrary constants, (CBSE 2018)

Question 5.

Solve the differential equation
cos\(\left(\frac{d y}{d x}\right)\) = a,(a ? R) (CBSE 2018 C)

Question 6.

Find the particular solution of the differential equation e^x tany dx + (2 – e^x) sec² y dy = 0, given that y = \(\frac{\pi}{4}\) when x = 0. (CBSE 2018)

Question 7.

Find the particular solution of the differential equation \(\frac{d y}{d x}\) + 2y tan x = sin x dx given that y = 0, when x = \(\frac{\pi}{3}\) (CBSE 2018; Foreign 2014)

Question 8.

Solve the differential equation (x² – y²) dx + 2xydy = 0. (CBSE 2018 C)

Question 9.

Show that the family of curves for which
\(\frac{d y}{d x}=\frac{x^{2}+y^{2}}{2 x y}\) is given by x² – y² = cx. (Delhi 2017)

Question 10.

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where c is a parameter. (Delhi 2017)