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Differential Equations

Kerala Board · Class 12 · Mathematics

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

35 questions20 flashcards5 concepts

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A diagram illustrating the components of a differential equation, showing independent variable, dependent variable, and derivatives. Examples of Ordinary Differential Equations (ODEs) are included.
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Key Topics to Revise

1

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)
2

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
3

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
4

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

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Full Notes

Key Concepts

A differential equation is an equationAn ordinary differential equation (ODE) involvesThe order is the highest derivativeThe degree is the highest powerA general solution contains arbitrary constants

Frequently Asked Questions

What are the important topics in Differential Equations for Kerala Board Class 12 Mathematics?
Differential Equations covers several key topics that are frequently asked in Kerala 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 — Kerala 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.

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All 13 chapters — Kerala Board Class 12 Mathematics Revision Notes

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