Consider the initial value problem 3u" - u' + 2u = o, u(0) = 4, u'(o) = 0. (a) Find the solution u(t) of this problem. V23 cos sin 23 u(t) - (b) For t> 0, find the first time at which Ju(t)| = 10. (A computer algebra system is recommended. Round your answer to four decimal places.) t-(6.779295 Additional Materials DeBook DETAILS BOYCEDIFFEQ10 3.3.036. An equation of the form p. a+ By = 0, t> 0, (1) dt dt where a and ß are real constants, is called an Euler equation. If we let x = In t and calculate dy/dt and dy/dt in terms of dyldx and d'yldx", then equation (1) becomes + (a - 1 + By - 0. (2) Observe that equation (2) has constant coefficients. If y (x) and y,(x) form a fundamental set of solutions of equation (2), then y;(In t) and y,(In t) form a fundamental set of solutions of equation (1). Use the method above to solve the given equation for t> 0. ty" + Sty' + 3y -0 y(t) -
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