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Differential Equations

Telangana Open School (TOSS) · Class 12 · Mathematics

Quick revision notes for Differential Equations — Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

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1. Basics of Differential Equations

  • A differential equation involves derivatives of a dependent variable with respect to an independent variable.
  • The order of a differential equation is the highest derivative present.
  • The degree is the power of the highest-order derivative, provided the equation is free from radicals and fractions involving derivatives.
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2. Formation of Differential Equations

  • To form a differential equation from a given family of curves, eliminate arbitrary constants by differentiation.
  • Number of times to differentiate = number of arbitrary constants.
  • Final equation must not contain any arbitrary constants.
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3. General and Particular Solutions

  • General solution contains arbitrary constants equal in number to the order of the equation.
  • Particular solution is obtained by assigning specific values to arbitrary constants using initial conditions.
  • Verification of solution involves substituting back into the original equation.
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4. Methods of Solving Differential Equations

  • Separation of variables: used when equation can be written as f(y)dy = g(x)dx.
  • Homogeneous equations: solved by substitution y = vx or x = vy.
  • Linear differential equations: solved using integrating factor (I.F.).

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Full Notes

Key Concepts

The order of a differential equationTo form a differential equation fromA general solution contains arbitrary constantsDifferent types of differential equations requireA differential equation is linear if

Frequently Asked Questions

What are the important topics in Differential Equations for Telangana Open School (TOSS) Class 12 Mathematics?
Differential Equations covers several key topics that are frequently asked in Telangana Open School (TOSS) 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 — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 50 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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