The Airy functions come from reducing the order of the equation to 2. Here is an example of this type. The exponential terms in the solution come from the general solution to the homogeneous equation, and the remaining term is a particular solution or particular integral to the problem.

## Differential Equations

This particular solution is part of the general solution to the inhomogeneous equation. Here is a nonlinear third-order ODE with no explicit dependence on or. It is solved by reducing the order to 2 using a simple integration.

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## Stability of higher-order nonlinear impulsive differential equations

Prerequisites MTH Learning Outcomes Upon successful completion of this subject, students should: Be able to select and apply appropriate techniques to solve these important classes of differential equations: separable, homogeneous, first order linear, higher order linear with constant coefficients, Bernoulli, Bessel's and Legendre's equations; Be able to investigate various phenomena by using relevant ODEs; Be able to use Laplace transforms and power series to solve linear ODEs; Be able to investigate the convergence of a solution given by a power series.

Syllabus This subject will cover the following topics: Partial derivatives: differentials, total derivative, test for exactness of first order ODEs.

Ordinary vs. Linear vs.

Homogeneous vs. ODE have been dealt with in Year-1 but we will have a brief review. Non-linear differential equations will not be discussed here.

There are specialist maths lectures on this topic. Blame me, not my employer etc.

- Second Order Differential Equations Calculator - Symbolab.
- Examples for!
- Differential Equations.
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