Definitions [3]
An equation involving independent variable(s), dependent variable(s), derivatives of the dependent variable (s) with respect to the independent variable(s), and a constant is called a differential equation.
The order of the highest differential coefficient (or the highest order derivative appearing in a differential equation) is the order of the differential equation.
The highest exponent of the highest derivative is called the degree of a differential equation, provided exponents of each derivative and an unknown variable appearing in the differential equation are non-negative integers.
Key Points
1. Basic Idea:
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Form a differential equation from a given equation by eliminating arbitrary constants
2. Steps:
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Identify arbitrary constants in the given equation
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Differentiate the equation with respect to x as many times as the number of constants
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Eliminate constants from the obtained equations
3. Important Rule:
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Number of differentiations = number of arbitrary constants
4. Final Result:
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After eliminating constants → required differential equation is obtained
6. Important Note:
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A differential equation represents a family of curves
Concepts [8]
- Introduction to Ordinary Differential Equations
- Order and Degree of a Differential Equation
- Classification of Differential Equations
- Formation of Differential Equations
- Solution of Ordinary Differential Equations
- Solution of First Order and First Degree Differential Equations
- First Order Linear Differential Equations
- Applications of First Order Ordinary Differential Equations
