Class 12 Mathematics — Chapter 3: DIFFERENTIAL EQUATIONS

What you'll learn

• ▸Order and Degree of a Differential Equation
• ▸General and Particular Solutions
• ▸Verification of Solutions
• ▸Formation of Differential Equations
• ▸Solving by Variables Separable Method
• ▸Solving Homogeneous Differential Equations
• ▸Solving Linear Differential Equations
• ▸Applications of Differential Equations

Chapter Summary

--- PAGE 1 --- 12080CH09 Chapter 9 DIFFERENTIAL EQUATIONS ❖ He who seeks for methods without having a definite problem in mind seeks for the most part in vain. – D. HILBERT ❖ 9.1 Introduction In Class XI and in Chapter 5 of the present book, we discussed how to differentiate a given function f with respect to an independent variable, i.e., how to find f '(x) for a given function f at each x in its domain of definition. Further, in the chapter on Integral Calculus, we discussed how to find a function f whose derivative is the function g, which may also be formulated as follows: For a given function g, find a function f such that dy — = g(x), where y = f(x) ... (1) dx An equation of the form (1) is known as a differential equation. A formal definition will be given later. Henri Poincare (1854-1912 ) …

Practice Questions from this Chapter

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1. Explain differential equations simply. Get Solution →
2. Give a real-world differential equation example. Get Solution →
3. Show how derivatives connect to change. Get Solution →
4. An equation involving the derivative of a dependent variable with respect to an independent variable is called what? Get Solution →
5. What is the 'order' of a differential equation? Get Solution →
6. For the degree of a differential equation to be defined, what must be true about the equation? Get Solution →
7. A solution to a differential equation that is free from arbitrary constants is known as what? Get Solution →
8. What is a solution to a differential equation that contains arbitrary constants called? Get Solution →

Did you know?

• 💡 Differential equations help predict everything from population growth to earthquake movements.
• 💡 Isaac Newton invented differential equations to understand how objects move and change speed.
• 💡 The way heat spreads through a metal bar is precisely described by a special differential equation.
• 💡 Doctors use differential equations to model how medicine travels through your body over time.
• 💡 Even the patterns on a leopard's skin can be explained using advanced forms of differential equations.

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