Special Case of Partial Fraction Expansion with Laplace Transform Application

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which inverse Transform can be easily found. This paper demonstrates a special case linear, constant coefficient, second order ordinary differential equation no damping term and harmonic function non-homogeneous leads simplified partial due decoupling of coefficients s coefficients. Recognizing this form allow quicker calculations automation solution commonly model physical systems.