Class 12 Maths - CBSE
Differential Equations
The chapter 'Differential Equations' in Class 12 Mathematics bridges calculus and real-world problem-solving by teaching how to model rates of change. You will learn to find the order and degree of differential equations, and master methods to solve First Order and First Degree equations, including Variable Separable, Homogeneous, and Linear Differential Equations. In CBSE board exams, this is a high-scoring chapter that frequently features direct computational problems as well as important word problems based on exponential growth, decay, and geometry.
Start Learning FreeKey Concepts
Order and Degree
The order of a differential equation is the order of the highest derivative involved, while the degree is the highest power of the highest-order derivative after the equation is made polynomial in derivatives.
General and Particular Solutions
A solution containing arbitrary constants is the general solution, whereas a solution free from arbitrary constants obtained by applying given conditions is a particular solution.
Variable Separable Method
A technique used when variables can be completely isolated on opposite sides of the equation, allowing integration on both sides.
Homogeneous Differential Equations
Equations where every term is of the same degree, solved by substituting y = vx or x = vy.
Linear Differential Equations
Equations of the form dy/dx + Py = Q, solved using an Integrating Factor (I.F.) given by e raised to the integral of P dx.
Important Formulas
Board Exam Info
In the CBSE Class 12 Mathematics board exam, Differential Equations typically carries around 7 to 10 marks. Common question types include 1-mark questions on finding order and degree, 2-mark or 3-mark questions on solving variable separable or homogeneous equations, and a mandatory 5-mark long-answer question based on solving a Linear Differential Equation or finding a particular solution.
Frequently Asked Questions
How do I know if a differential equation is homogeneous?
Replace x with kx and y with ky in the function f(x,y). If you can factor out k^n (where n is the degree) to get back the original function k^n * f(x,y), it is homogeneous.
What is the difference between order and degree?
Order is simply how many times you differentiate (highest derivative), while degree is the exponent of that highest derivative, provided the equation is a polynomial in its derivatives.
When do I include the constant +C in my solution?
You must add +C (the constant of integration) as soon as you perform indefinite integration on both sides of the equation. For particular solutions, you use the given initial conditions to find the exact value of C.
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