Differential Equations — Revision Notes
MHT-CET · Mathematics
Quick revision notes for Differential Equations — key concepts, formulas, and definitions for MHT-CET Mathematics preparation.
Revision Notes — Differential Equations
Key concepts, formulas, and definitions from Differential Equations for MHT-CET Mathematics preparation.
Key Topics to Revise
Basic Concepts and Definitions
- A differential equation involves derivatives of dependent variables with respect to independent variables
- Order is determined by the highest derivative present
- Degree is the power of the highest order derivative (when polynomial form)
Formation of Differential Equations
- To form differential equation from general solution, differentiate and eliminate arbitrary constants
- Number of differentiations = number of arbitrary constants
- Final equation should be free from arbitrary constants
Variable Separable Method
- Applicable when equation can be written as dy/dx = f(x)g(y)
- Separate variables: dy/g(y) = f(x)dx
- Integrate both sides and add constant of integration
Homogeneous Differential Equations
- Equation of form dy/dx = f(x,y)/g(x,y) where f,g are homogeneous functions of same degree
- Substitute y = vx, so dy/dx = v + x(dv/dx)
- Equation becomes separable in variables v and x
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Key Concepts
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What topics are covered in Differential Equations for MHT-CET?
Differential Equations is an important chapter in MHT-CET Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Concepts and Definitions, Formation of Differential Equations, Variable Separable Method, Homogeneous Differential Equations.
How important is Differential Equations for MHT-CET?
Differential Equations is a frequently tested chapter in MHT-CET Mathematics. Questions from this chapter appear regularly in previous year papers. There are 50 practice questions available for this chapter.
How to prepare Differential Equations for MHT-CET?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.