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Second Order Linear Equations
In each of Problems 1 through8 find the general solution of the given differential equation.
Then determine the maximum value of the solution and also
find the point where the
solution is zero .
21. Solve the initial value problem . Then find α so that
the solution approaches zero as .
22. Solve the initial value problem. Then find β so that the
solution approaches zero as .
In each of Problems 23 and 24 determine the value of α if any . for which al l solutions tend to
zero as : also determine the values of α. if any , for which all (nonzero) solutions become
25. Consider the initial value problem
where β > 0.
(a) Solve the initial value problem.
(b) Plot the solution when β= 1. Find the coordinates f the minimum point of
the solution in this case.
(c) Find the smallest value of β for which the solution has no minimum point.