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Answer: In each of 7 through 12, find the solution of the given initial value problem
Chapter 3, Problem 7(choose chapter or problem)
In each of 7 through 12, find the solution of the given initial value problem. Sketch the graph of the solution and describe its behavior as t increases. y__ + y_ 2y = 0, y(0) = 1, y_(0) = 1 G
Questions & Answers
QUESTION:
In each of 7 through 12, find the solution of the given initial value problem. Sketch the graph of the solution and describe its behavior as t increases. y__ + y_ 2y = 0, y(0) = 1, y_(0) = 1 G
ANSWER:Step 1 of 4
The objective is to find the general solution for the following initial value problem:
,
Assume that is a solution of the homogeneous equation.
Find the first and second derivative of the function.
Substitute the values, , and in .
Since, then
Thus, the characteristic equation for the differential equation is.