Class 12 Maths - BIHAR
Differential Equations
The Differential Equations chapter in Class 12 Mathematics for Bihar Board (BSEB) students explores equations involving derivatives of a dependent variable with respect to an independent variable. You will learn to find the order and degree of a differential equation, and solve them using various methods such as variable separable, homogeneous differential equations, and linear differential equations. This chapter is extremely high-scoring and vital for both objective and subjective sections in the BSEB board examinations, often featuring direct integration-based word problems and long-answer questions that test your calculus mastery.
Start Learning FreeKey Concepts
Order and Degree of Differential Equation
The order is the highest derivative present in the equation, 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 to solve first-order differential equations by grouping all terms containing the 'x' variable with dx and all 'y' terms with dy on opposite sides.
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 form.
Linear Differential Equations
Equations of the form dy/dx + Py = Q (where P and Q are functions of x) solved using an Integrating Factor (IF) equal to e^(integral P dx).
Important Formulas
Board Exam Info
In the Bihar Board (BSEB) Class 12 Mathematics exam, Differential Equations typically carries around 10 to 15 marks. Questions appear in all formats: objective (MCQs on order and degree), short-answer (solving variable separable or homogeneous equations), and long-answer (solving linear differential equations or finding particular solutions).
Frequently Asked Questions
How do I find the degree if a radical or trigonometric function contains a derivative?
The differential equation must first be expressed as a polynomial equation in derivatives. If the highest derivative appears inside a sine, cosine, or fractional power that cannot be cleared, the degree is not defined.
Is it compulsory to add constant 'C' in the general solution?
Yes, adding the arbitrary constant 'C' is mandatory for the general solution. Forgetting to write '+ C' will result in a deduction of marks in BSEB subjective questions.
How do I identify 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), the equation is homogeneous.
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