Chapter 2.3, Problem 57E

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:

$\begin{array}{l}\frac{dx}{dt}=-{\lambda }_{1}x\\ \frac{dy}{dt}={\lambda }_{1}x-{\lambda }_{2}y,\end{array}$

where λ₁ and λ₂ are constants. Discuss how to solve this system subject to x(0) = x₀, y(0) = y₀. Carry out your ideas.