Solving differential equations of the form dy/dx = f(x) (HSC SSCE Mathematics Extension 1): Quizzes

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Solving Differential Equations of the Form dy/dx = f(x)
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What is a differential equation?

An equation with derivatives

What does integration do?

Finds original functions

What is a general solution?

Solution with constants

What is a particular solution?

Solution with initial values

How do you solve rac{dy}{dx} = f(x)?

Integrate both sides

What is the result of integrating 3x23x^2 with respect to x?

x^3 + C

What is the particular solution for y(0)=1y(0) = 1?

y = e^x

How do you verify a solution?

Substitute y into the equation

What does rac{dT}{dt} = -kT model?

Temperature change

Why are differential equations important?

They model changes

Explore HSC SSCE Mathematics Extension 1 Revision Notes by Topics

Direction fields

Introduction to differential equations

Modelling with first-order differential equations

Solving differential equations of the form dy/dx = f(x)

Solving differential equations of the form dy/dx = g(y)

Solving differential equations using separation of variables

Explore HSC SSCE Mathematics Extension 1 Model Answers by Topics

Direction fields

Introduction to differential equations

Modelling with first-order differential equations

Solving differential equations of the form dy/dx = f(x)

Solving differential equations of the form dy/dx = g(y)

Solving differential equations using separation of variables

Explore HSC SSCE Mathematics Extension 1 Flashcards by Topics

Direction fields

Introduction to differential equations

Modelling with first-order differential equations

Solving differential equations of the form dy/dx = f(x)

Solving differential equations of the form dy/dx = g(y)

Solving differential equations using separation of variables

Explore HSC SSCE Mathematics Extension 1 Exam Questions by Topics

Direction fields

Introduction to differential equations

Modelling with first-order differential equations

Solving differential equations of the form dy/dx = f(x)

Solving differential equations of the form dy/dx = g(y)

Solving differential equations using separation of variables

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