Abstract
In this research work Complex Differential Equations of order two was studied and then solved using the Laplace transform technique. The Complex Differential Equations were separated into the real and imaginary parts and an expression for the solution form of the complex differential equation of order two with constant coefficient was obtained. The solution to the problems were then obtained using Laplace technique. The real and imaginary parts of the solution were further obtained using the inverse Laplace transform giving the results for the problem, and also illustrative examples are included to demonstrate the validity and applicability of the expression for the solution form of the problems
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