Flashcards: Fundamentals of Differential Equations — 10 cartões

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1Pergunta

ODE — definition?

Resposta

Equation involving derivatives of one variable.

2Pergunta

ODE — definition?

Resposta

Equation involving derivatives of one variable.

3Pergunta

Order of ODE — what?

Resposta

Highest derivative present in the equation.

4Pergunta

Order of an ODE — what?

Resposta

Highest derivative present in the equation.

5Pergunta

First-order equations — role?

Resposta

Model dynamic systems with first derivatives.

6Pergunta

Degree of an ODE — definition?

Resposta

Highest power of derivatives when polynomial form.

7Pergunta

Linear ODE — key feature?

Resposta

Function and derivatives appear to the first power.

8Pergunta

Nonlinear ODE — characteristic?

Resposta

Derivatives or functions are multiplied or powers.

9Pergunta

Solution of an ODE — what?

Resposta

Function satisfying the equation for all relevant in t.

10Pergunta

Differentiation — role in ODEs?

Resposta

Describes how a function changes with t.

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1. Which theorem guarantees both the existence and uniqueness of solutions to an initial value problem for an ordinary differential equation?

2. What is the defining characteristic of a linear ordinary differential equation (ODE)?

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