# Second-order differential equations

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Learn how to solve linear constant-coefficient second-order differential equations with this free course. Understand the principles and methods involved, including finding general solutions and using extra information. Gain insights into resonance and obtain particular solutions. Ideal for those seeking a comprehensive understanding.

This free course is concerned with second-order differential equations. Section 1 introduces some basic principles and terminology. Sections 2 and 3 give methods for finding the general solutions to one broad class of differential equations, that is, linear constant-coefficient second-order differential equations. Section 2 covers homogeneous equations and Section 3 covers inhomogeneous equations. Section 4 explains how extra information can be used to help to select particular solutions that are appropriate in given situations. Section 5 looks at the phenomenon of resonance to gain insights into the solutions of inhomogeneous linear constant-coefficient second-order differential equations.

## Course learning outcomes

After studying this course, you should be able to:

Understand the key role of the principle of superposition in the solution of linear constant-coefficient second-order differential equations

Obtain the general solution of a homogeneous linear constant-coefficient second-order differential equation using the solutions of its auxiliary equation

Use the method of undetermined coefficients to find a particular integral for an inhomogeneous linear constant-coefficient second-order differential equation with certain simple forms of right-hand-side function

Obtain the general solution of an inhomogeneous linear constant-coefficient second-order differential equation by combining its complementary function with a particular integral

Use the general solution together with a pair of initial or boundary conditions to obtain, when possible, a particular solution of a linear constant-coefficient second-order differential equation.

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