Consider the initial value problem
4u'' − u' + 2u = 0, u(0) = 3, u'(0) = 0.
(a) Find the solution u(t) of this problem.
(b) For t > 0, find the first time at which |u(t)| = 10. Round your answer to four decimal places.

Answer with Step-by-step explanation:

We are given that initial value problem

a.

u(0)=3,u'(0)=0

Auxillary equation

By using quadratic formula:

Therefore, the general solution of the initial value problem

Substitute t=0 and u(0)=3

Differentiate w.r.t t

Substitute t=0 and u'(0)=0

Substitute the value of

Substitute the values

(b) For t>0

We cannot find the solution of  analytically

But we can use the graph to find the approximate value of the solution.

By graph , the approximate value of t=12.2 for which  

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step-by-step explanation: