Differential Equations
Madhya Pradesh Board · Class 12 · Mathematics
Summary of Differential Equations for Madhya Pradesh Board Class 12 Mathematics. Key concepts, important points, and chapter overview.
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Differential equations connect a function with its derivatives. They are used to describe how quantities change and how a curve or function can be determined from a relation involving derivatives. The chapter begins with the basic idea of an equation containing derivatives of the dependent variable
Key Concepts
An equation involving derivatives of
An equation involving derivatives of the dependent variable with respect to an independent variable is called a differential equation. The basic form
A differential equation involving derivatives
A differential equation involving derivatives with respect to only one independent variable is an ordinary differential equation.
The order is the order
The order is the order of the highest order derivative present in the equation. For example, equations with highest derivatives of first, second, and
Degree is defined only when
Degree is defined only when the equation is a polynomial in derivatives. It is the highest power of the highest order derivative. If the equation is n
The solution containing arbitrary constants
The solution containing arbitrary constants is the general solution or primitive of the differential equation.
Learning Objectives
- Define a differential equation and distinguish it from ordinary algebraic equations.
- Identify ordinary differential equations and understand that partial differential equations involve more than one independent variable.
- Determine the order and degree of a differential equation.
- Distinguish between general solution and particular solution.
- Solve first order differential equations by the variable separable method.
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