Solution Found!
In each of 8 through 12, proceed as in 7.(a) Transform the given system into a single
Chapter 7, Problem 9(choose chapter or problem)
In each of Problem, proceed as in Problem 7.
(a) Transform the given system into a single equation of second order.
(b) Find \(x_1\) and \(x_2\) that also satisfy the given initial conditions.
(c) Sketch the graph of the solution in the \(x_{1} x_{2}\)-plane for \(t \geq 0\).
\(\begin{array}{ll}
x_{1}^{\prime}=1.25 x_{1}+0.75 x_{2}, & x_{1}(0)=-2 \\
x_{2}^{\prime}=0.75 x_{1}+1.25 x_{2}, & x_{2}(0)=1
\end{array}\)
Questions & Answers
QUESTION:
In each of Problem, proceed as in Problem 7.
(a) Transform the given system into a single equation of second order.
(b) Find \(x_1\) and \(x_2\) that also satisfy the given initial conditions.
(c) Sketch the graph of the solution in the \(x_{1} x_{2}\)-plane for \(t \geq 0\).
\(\begin{array}{ll}
x_{1}^{\prime}=1.25 x_{1}+0.75 x_{2}, & x_{1}(0)=-2 \\
x_{2}^{\prime}=0.75 x_{1}+1.25 x_{2}, & x_{2}(0)=1
\end{array}\)
Step 1 of 7
An auxiliary equation is an equation obtained from the standard form of a linear differential equation by replacing the right member with zero.