PROBLEM 52E

Radioactive Decay Series The following system of differential equations is encountered in the study of the decay of a special type of radioactive series of elements:

where are constants. Discuss how to solve this system subject to x(0) = x0, y(0) = y0. Carry out your ideas.

In this question we have to solve the equation and where and are constants subject to

Step 1 </p>

Solving the first differential equation

Separating the variables

Integrating both sides

For the initial condition

=>

Substituting the value in , we get