Conclusion

Following completion of this free OpenLearn course, Second-order differential equations, as well as being able to ‘appreciate the importance of the role that linear constant-coefficient second-order differential equations play in physics and areas of applied mathematics’, you should also find that your skills in calculus are improving.

You should now 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.

This free OpenLearn course is an extract from the Open University course MST224 Mathematical methods [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

If you feel you are ready to move on in your study of applied mathematics but don’t have time to study a full Open University course at this time, you might like to study the free OpenLearn course Dynamics, an adapted extract from the Open University course MST210 Mathematical methods, models and modelling.

Alternatively, if you are interested in pure mathematics, you might like to try the free OpenLearn courses Introduction to group theory, Introduction to linear equations and matrices and Introduction to analysis. If you are interested in statistics, you might like to try the free OpenLearn courses Modelling and estimation, Medical statistics and Bayesian statistics.