We consider the second order linear differential equation $y = \left[ {\frac{{{ \wedge ^2}}}{{{t^\alpha }}}+ g\left( t \right)} \right]y,$ where Λ is a large complex ...

We give the existence and the analytic form of the solutions to the linear fractional differential equations in which coefficients are bounded function on [0, b]. The method which is used is based on ...

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Solve for the Laplace Transform of the Unknown Function: After applying the Laplace transform, the integral equation is ...