Final answer:
A differential equation is an equation that relates functions and their derivatives. The order of a differential equation refers to the highest derivative present in the equation. The degree of a differential equation refers to the highest power of the derivative present in the equation.
Step-by-step explanation:
A differential equation is an equation that relates functions and their derivatives. It is used to model real-world problems in various fields, such as physics and engineering. The order of a differential equation refers to the highest derivative present in the equation. The degree of a differential equation refers to the highest power of the derivative present in the equation. To form the differential equation whose solution is Y = e-x(Asinx + Bcosx), we differentiate Y with respect to x and find its highest derivative. In this case, the highest derivative is the second derivative, which is:
Y'' = -2e-x(Acosx + Bsinx).