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In this chapter we discuss the theory of initial value problems for ordinary differential equations. We limit ourselves to scalar equations here; systems will be discussed in the next chapter. After presenting the general definition of a differential equation and the geometric significance of its direction field, we start with a detailed discussion of first-order linear equations. As important applications we discuss the modelling of growth and decay processes. Subsequently, we investigate questions of existence and (local) uniqueness of the solution of general differential equations and discuss the method of power series. We also study the qualitative behaviour of solutions close to an equilibrium point. Finally, we discuss the solution of second-order linear problems with constant coefficients.
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- Differential Equations
- Springer International Publishing
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- Chapter number
- Chapter 19