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Ordinary Differential Equations

Tamil Nadu Board · Class 12 · Mathematics

Quick revision notes for Ordinary Differential Equations — Tamil Nadu Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

43 questions24 flashcards5 concepts

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A labeled diagram explaining the definitions of order and degree of a differential equation with illustrative examples.
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Key Topics to Revise

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1. Order and Degree of Differential Equations

  • A differential equation (DE) contains at least ONE derivative of an unknown function.
  • ORDER = the highest derivative present in the equation. It is always a positive integer.
  • DEGREE = the power of the highest order derivative, BUT ONLY after the equation is expressed in polynomial form (free from fractional powers, and highest derivative must NOT be inside a transcendental
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2. Classification: ODE, PDE, Linear, Nonlinear, Homogeneous

  • ODE (Ordinary Differential Equation): derivatives with respect to only ONE independent variable.
  • PDE (Partial Differential Equation): involves partial derivatives (two or more independent variables). NOT covered in this chapter.
  • Linear ODE: the unknown function y and ALL its derivatives appear to the FIRST POWER only, with NO products between y and its derivatives, NO transcendental functions OF y.
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3. Formation of Differential Equations

  • To form a DE from a family of curves with n arbitrary constants: differentiate n times and then eliminate all n constants.
  • Eliminating 1 constant → 1st order DE; eliminating 2 constants → 2nd order DE; eliminating n constants → nth order DE.
  • The number of arbitrary constants = the order of the resulting DE.
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4. General Solution and Particular Solution

  • A solution of a DE is an expression for the dependent variable satisfying the equation.
  • General Solution: contains as many arbitrary constants as the ORDER of the DE. Represents a family of solutions.
  • Particular Solution: obtained by substituting specific values for the arbitrary constants (using initial/boundary conditions).

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Full Notes

Key Concepts

A differential equation is any equationThe order is the highest derivativeThe degree is the highest powerA linear differential equation hasA linear differential equation is homogeneous

Frequently Asked Questions

What are the important topics in Ordinary Differential Equations for Tamil Nadu Board Class 12 Mathematics?
Key topics in Ordinary Differential Equations include Chapter 10: Ordinary Differential Equations — Complete Overview, Ordinary Differential Equations — Complete Mind Map, Differential Equation Solution Method Decision Tree. These are the concepts Tamil Nadu Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Ordinary Differential Equations — Tamil Nadu Board Class 12 Mathematics?
Understand the core concepts first, then work through the 43 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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