Class 12 Maths
Differential Equations
Question 1:
Determine order and degree (if defined) of differential equation (y′′′)2 + (y″)3 + (y′)4 + y5 = 0
Question 2:
Solve the differential equation: (x2 - 1) * dy/dx + 2xy = 2/(x2 - 1)
Question 3:
Form the differential equation representing the family of curves
y = a sin(x + b), where a, b are arbitrary constants.
Question 4:
Find the general solution of the differential equation dy/dx + √{(1 – y2)/(1 – x2)} = 0
Question 5:
Find the differential equation of the family of lines through the origin.
Question 6:
Find a particular solution of the differential equation (x - y)(dx + dy) = dx – dy, given that y = -1, when x = 0.
Question: 7
Form the differential equation representing the family of curves
y = a sin(3x – b), where a and b are arbitrary constants.
Question 8:
Find the general solution of the differential equation
cos(dy/dx) = a (a ∈ R); y = 1 when x = 0.
Question 9:
Find the general solution of the differential equation:
x * dy/dx + y – x + xy cot x = 0 (x ≠ 0)
Question 10:
Prove that (x2 - y2) = c(x2 - y2)2 is the general solution of differential equation
(x3 – 3xy2)dx = (y3 – 3x2y)dy, where c is a parameter.
Question 11:
Verify that the function y = a cos x + b sin x, where, a, b ∈ R is a solution of the differential equation d2y/dx2 + y = 0.
Question 12:
For each of the given differential equation, find a particular solution satisfying the given condition: dy/dx = y * tan x; y = 1 when x = 0
Question 13:
Find the general solution of the differential equation dy/dx = (1 + y2)/(1 + x2).
Question 14:
Integrating factor of the differential equation (1 – x2)dy/dx – xy = 1 is ____.
Question 15:
Determine order and degree (if defined) of differential equation
y’’’ + 2y’’ + y’ = 0
Question 16:
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = √(1 + x2) : y’ = xy/(1 + x2)
Question 17:
Solve: cos(dy/dx) = a (a ∈ R); y = 1 when x = 0
Question 18:
Solve: dy/dx = 1 + x + y + xy
Question 19:
Write the general solution of differential equation:
dy/dx = ex+y
Question 20:
Form the differential equation representing the family of curves:
y = e2x(a + bx), where ‘a’ and ‘b’ are arbitrary constants.
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In summary, problem-solving after learning a theoretical concept on CBSE Differential Equations Class 12 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.
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Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.
All About Daily Practice Problems on Class 12 Maths Differential Equations NCERT Chapter 9
Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 12 Maths Differential Equations NCERT Chapter 9 useful.
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