Differential Equations Flashcards

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Questions and Answers

What is an Ordinary Differential Equation (ODE)?

  • A differential equation containing unknown multivariable functions
  • A differential equation containing one or more functions of one independent variable and its derivatives (correct)
  • A differential equation that cannot be classified
  • A differential equation only of constant coefficients

What is a Partial Differential Equation (PDE)?

  • A differential equation containing unknown multivariable functions and their partial derivatives (correct)
  • A differential equation that involves only one variable
  • A type of linear differential equation
  • A simple algebraic equation

What are Systems of Differential Equations?

Models that involve several functions, all connected by differential equations.

What does the 'Order' of a differential equation refer to?

<p>The order of the highest derivative that appears in the equation.</p> Signup and view all the answers

What is a Linear ODE?

<p>A differential equation that can be written as a linear combination of y, y', y'', etc. (B)</p> Signup and view all the answers

What is a Nonlinear ODE?

<p>A differential equation that cannot be written as a linear combination of y, y', y'', etc. (D)</p> Signup and view all the answers

What is a Solution on an interval (a, b)?

<p>A function y(t) that satisfies the general ODE equation F(t, y,...y^(n))=0 for all t in (a, b).</p> Signup and view all the answers

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Study Notes

Types of Differential Equations

  • Ordinary Differential Equation (ODE): Involves functions of a single independent variable and their derivatives.
  • Partial Differential Equation (PDE): Involves unknown functions of multiple independent variables and their partial derivatives.
  • Systems of Differential Equations: Consists of interconnected differential equations involving several dependent functions.

Key Terms

  • Order: Defined by the highest derivative present in the differential equation, determining its complexity.
  • Linear ODE: Can be expressed as a linear combination of the dependent variable and its derivatives, with coefficients being functions of the independent variable.
  • Nonlinear ODE: Cannot be expressed as a linear combination of the dependent variable and its derivatives, indicating a more complex relationship.

Solutions

  • Solution on an interval (a, b): A function that satisfies the ordinary differential equation for all values of the independent variable within the specified interval.

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