Mathematics chapters
  1. 013D Geometry
  2. 02Application of Derivatives
  3. 03Area Under Curves
  4. 04Binomial Theorem
  5. 05Circles
  6. 06Complex Numbers
  7. 07Continuity & Differentiability
  8. 08Definite Integration
  9. 09Determinants
  10. 10Differential Equations
  11. 11Ellipse
  12. 12Hyperbola
  13. 13Indefinite Integration
  14. 14Inequalities & Modulus
  15. 15Inverse Trigonometric Functions
  16. 16Limits
  17. 17Logarithms
  18. 18Matrices
  19. 19Methods of Differentiation
  20. 20Number System & Basics
  21. 21Parabola
  22. 22Permutations & Combinations
  23. 23Probability
  24. 24Properties of Triangle
  25. 25Quadratic Equations
  26. 26Sequences & Series
  27. 27Sets, Relations & Functions
  28. 28Statistics
  29. 29Straight Lines
  30. 30Trigonometric Equations
  31. 31Trigonometric Ratios & Identities
  32. 32Vectors

Chapter 10 · Class 11-12 & JEE Main/Adv

Differential Equations

25 topics in 12 parts

Full lessonClass 12 Mathematics · Differential Equations
Order of a Differential Equation Degree of a Differential Equation General Solution Particular Solution Formation by Eliminating Constants Separable Equation

Key ideas

+Y +Z +X O(0,0,0) Line L A(x₁, y₁, z₁) a P(x, y, z) r Parallel Vector b = aî + bĵ + ck̂ Cartesian Form: (x - x₁)/a = (y - y₁)/b = (z - z₁)/c = λ ⟺ General Point: (x₁ + λa, y₁ + λb, z₁ + λc)
Differential Equations

Analytical Comparison & Distinction Matrix

Analytical MethodStandard RepresentationParametric / Invariant Framework
Algebraic NatureExplicit equations relating spatial coordinatesParameterized using scalar parameters (λ, μ) or vectors
Symmetry UsageRelies on coordinate expansionExploits vector dot/cross products for rapid simplification
Computational EfficiencyDirect for intercept evaluationSuperior for angles, orthogonal projections, and distances
Common MistakeSign confusion in determinantsOmitting boundary condition checks

All 25 topics in Differential Equations

  1. Differential Equation of First Order & First Degree

    • Order & Degree of Differential Equations

  2. Formation of Differential Equations

    • Elimination of Arbitrary Constants
    • Differential Equation of a Family of Curves

  3. Solution of Differential Equations

    • Initial Value Problems
    • Solution Curves & Qualitative Analysis
    • Functional Relations
    • Cauchy-Euler Equation
    • Clairaut Equation

  4. Method of Variable Separation

    • General Form of Variable Separation
    • Differential Equations Reducible to the Variable Separation Type

  5. Homogeneous Equations

    • Standard Homogeneous Form
    • Differential Equations Reducible to Homogeneous Form

  6. Linear Differential Equations

    • First-Order Linear Equations
    • Bernoulli's Equation
    • Equations Linear in x
    • Differential Equations Reducible to Linear Form

  7. Exact Differential Equations

    • Integrating Factors for Non-Exact Equations

  8. Substitution Methods

    • Change of Dependent or Independent Variable

  9. Polar Coordinate Method

    • Polar Coordinates Substitution

  10. Integral-Differential Equations

    • Integral Equations Reducible by Differentiation

  11. Geometrical Applications of Differential Equation

    • Trajectories
    • Tangent & Normal Properties
    • Families of Curves

  12. Applications of Differential Equations

    • Population Growth & Spread
    • Rates & Physical Models