Establish first that y(t) = aet + bet+c cosh(t) + d sinh(t) solves the differential equation,...

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Establish first that y(t) = aet + bet+c cosh(t) + d sinh(t) solves the differential equation, d²y dt² (t)- y(t) = 0. This solution contains four different homogeneous solutions when we know that we need only two. To understand why two extra solutions are unnec- essary, apply the initial conditions y (0) = A, and There are two equations for four unknown coefficients. Determine c and d in terms of A, B, a and b and substitute the results into the solution. What is the consequence? What does it tell you about the number of independent solutions needed to satisfy the initial conditions? dy dt (0) = B. Establish first that y(t) = aet + bet+c cosh(t) + d sinh(t) solves the differential equation, d²y dt² (t)- y(t) = 0. This solution contains four different homogeneous solutions when we know that we need only two. To understand why two extra solutions are unnec- essary, apply the initial conditions y (0) = A, and There are two equations for four unknown coefficients. Determine c and d in terms of A, B, a and b and substitute the results into the solution. What is the consequence? What does it tell you about the number of independent solutions needed to satisfy the initial conditions? dy dt (0) = B.

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Answer Hence solved it Letyt ae beccosh t d sinh t Then and aebec cosh td sinh t ae be... View the full answer