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Differential Equations — Syllabus

Madhya Pradesh Board · Class 12 · Mathematics

What Differential Equations covers in Madhya Pradesh Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

94 questions50 flashcards17 formulas & key relations5 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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4 Topics · Madhya Pradesh Board Class 12 Mathematics · 2026-27

Topics in Differential Equations

1

1. Basic Ideas, Order, and Degree

  • A differential equation involves derivatives of the dependent variable with respect to an independent variable.
  • An ordinary differential equation involves derivatives with respect to only one independent variable.
  • Partial differential equations involve more than one independent variable and are not studied here.
2

2. General Solution and Particular Solution

  • A solution of a differential equation is a function that satisfies it.
  • A solution curve is also called an integral curve.
  • A general solution contains arbitrary constants.
3

3. Variable Separable Differential Equations

  • A first order first degree differential equation can be solved by separation when it can be written as a product of a function of x and a function of y.
  • The variable separable form is dy/dx = h(y)·g(x).
  • After separation, write all y-terms with dy and all x-terms with dx.
4

4. Homogeneous Differential Equations

  • A function F(x,y) is homogeneous of degree n if F(λx, λy) = λ^n F(x,y) for nonzero λ.
  • F1(x,y)=y^2+2xy is homogeneous of degree 2.
  • F2(x,y)=2x-3y is homogeneous of degree 1.

Key Concepts

Central concept: Differential Equations

Meaning and definitionOrderDegreeSolution of a differential equationGeneral and particular solutionsVariable separable methodHomogeneous differential equationsLinear differential equations

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Frequently Asked Questions

What are the important topics in Differential Equations for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Differential Equations include Basic Ideas, Order, and Degree, General Solution and Particular Solution, Variable Separable Differential Equations, Homogeneous Differential Equations. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Differential Equations for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 94 practice questions on Differential Equations. Revise 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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All Madhya Pradesh Board Class 12 Mathematics Syllabus

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