Chapter 8 of 12
Revision Notes
Ordinary Differential Equations — Revision Notes
Tamil Nadu Board · Class 12 · Mathematics
Ordinary Differential Equations revision notes for Tamil Nadu Board Class 12 Mathematics: 4 topics in quick points.
43 questions24 flashcards3 formulas & key relations5 concepts
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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 NotesKey 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 Order and Degree of Differential Equations, Classification: ODE, PDE, Linear, Nonlinear, Homogeneous, Formation of Differential Equations, General Solution and Particular Solution. Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
How should I revise Ordinary Differential Equations for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 43 practice questions on Ordinary Differential Equations. Revise definitions regularly and use flashcards for quick recall before the exam.
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