Differential Equations
Uttar Pradesh Board · Class 12 · Mathematics
Quick revision notes for Differential Equations — Uttar Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Concepts and Definitions
- A differential equation is an equation involving derivatives of the dependent variable with respect to independent variable(s)
- Ordinary differential equations involve derivatives with respect to only one independent variable
- Partial differential equations involve derivatives with respect to more than one independent variable (not in syllabus)
General and Particular Solutions
- Solution of a differential equation is a function that satisfies the equation
- General solution contains arbitrary constants equal to the order of the equation
- Particular solution is obtained by assigning specific values to arbitrary constants
Variable Separable Method
- Used when dy/dx = f(x)g(y) or can be written in this form
- Separate variables: terms with y on one side, terms with x on other side
- Integrate both sides to get solution
Homogeneous Differential Equations
- Equation of form dy/dx = f(x,y) where f(x,y) is homogeneous function of degree zero
- f(λx, λy) = f(x,y) for all λ ≠ 0 (homogeneous function of degree zero)
- Substitute y = vx (where v is function of x) to solve
Get complete notes with diagrams and examples
Full NotesKey Concepts
Get detailed revision notes for Differential Equations
Super Tutor gives you interactive content for every chapter of Uttar Pradesh Board Class 12 Mathematics — summaries, quizzes, flashcards, and more.
Try Super Tutor — It's FreeFrequently Asked Questions
What are the important topics in Differential Equations for Uttar Pradesh Board Class 12 Mathematics?
Differential Equations covers several key topics that are frequently asked in Uttar Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Differential Equations — Uttar Pradesh Board Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More Resources for Differential Equations
Important Questions
Practice with board exam-style questions
Syllabus
What topics to cover
Study Plan
Step-by-step plan to ace this chapter
Flashcards
Quick-fire cards for active recall
Formula Sheet
All formulas in one place
Chapter Summary
Understand the chapter at a glance
Practice Quiz
Test yourself with a quick quiz
Concept Maps
See how topics connect visually