Solution Found!
ts: where are constants. Discuss how to solve this system
Chapter 2, Problem 52E(choose chapter or problem)
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:
\(\frac{d x}{d t}=-\lambda_{1} x\)
\(\frac{d y}{d t}=\lambda_{1} x-\lambda_{2} y\)
where \(\lambda_{1}\) and \(\lambda_{2}\) are constants. Discuss how to solve this system subject to \(x(0)=x_{0}\), \(y(0)=y_{0}\). Carry out your ideas.
Text Transcription:
dx/dt = -lambda_1 x
dy/dt=lambda_1 x - lambda_2 y
lambda_1
lambda_2
x(0)=x_0
y(0)=y_0
Questions & Answers
QUESTION:
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:
\(\frac{d x}{d t}=-\lambda_{1} x\)
\(\frac{d y}{d t}=\lambda_{1} x-\lambda_{2} y\)
where \(\lambda_{1}\) and \(\lambda_{2}\) are constants. Discuss how to solve this system subject to \(x(0)=x_{0}\), \(y(0)=y_{0}\). Carry out your ideas.
Text Transcription:
dx/dt = -lambda_1 x
dy/dt=lambda_1 x - lambda_2 y
lambda_1
lambda_2
x(0)=x_0
y(0)=y_0
ANSWER:Step 1 of 3
In this question we have to solve the equation and
where
and
are constants subject to