Class 12 Maths - ISC
Differential Equations
The Differential Equations chapter for Class 12 ISC mathematics builds upon calculus to model real-world phenomena involving rates of change. Students learn to determine the order and degree of equations, solve first-order first-degree differential equations using separation of variables, homogeneous equations, and linear differential equations. Mastering this chapter is crucial for scoring high in ISC board exams, as it consistently features high-weightage long-answer questions and integration-heavy problem-solving that test both analytical skills and computational accuracy.
Start Learning FreeKey Concepts
Order and Degree
The order of a differential equation is the highest derivative present, 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 general solution contains arbitrary constants equal in number to the order of the differential equation, whereas a particular solution is obtained by assigning specific values to these constants using given boundary conditions.
Variable Separable Method
A technique used to solve first-order differential equations by algebraically rearranging terms so that all functions of x and dx are on one side, and all functions of y and dy are on the other.
Homogeneous Differential Equations
Equations where every term is of the same degree, solved by substituting y = vx or x = vy to reduce them into variable separable forms.
Linear Differential Equations
First-order equations of the form dy/dx + Py = Q, solved using an integrating factor (IF) given by e^(integral P dx).
Important Formulas
Board Exam Info
In the ISC Class 12 Mathematics examination, Differential Equations typically carries around 8 to 12 marks. Questions usually include 1-mark or 2-mark objective questions on finding order and degree, and 4-mark or 6-mark subjective questions focusing on solving homogeneous, linear, or particular differential equations.
Frequently Asked Questions
How do I find the degree of a differential equation when trigonometric or exponential functions contain derivatives?
The degree is not defined if the differential equation cannot be expressed as a polynomial equation in terms of its derivatives (e.g., if a derivative is inside a sin, cos, or log function).
When should I use the integrating factor method instead of variable separable?
Use the integrating factor method when the first-order differential equation is linear in the dependent variable and cannot be rearranged into variable separable form.
Do I always need to add the constant 'C' in the general solution?
Yes, adding the constant of integration 'C' is mandatory for general solutions, and omitting it will result in loss of marks in the ISC board exam.
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