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Question: consider the following differential equation a computer algebra system is...

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Consider the following differential equation. (A computer algebra system is recommended.) (a) Draw a direction field for the qiven differential equation.(b) Based on an inspection of the direction field, describe how solutions behave for large t If y(o)> - 9, solutions eventually have positive slopes, and hence increase without bound. If y(0) s - 9, solutions have negative slopes and decrease without bound The solutions appear to be oscillatory. If y(0) , solutions eventually have positive slopes, and hence increase without bound. If y(0) > All solutions seem to converge to the function yo(t)0 All solutions seem to eventually have positive slopes, and hence increase without bound. solutions have negative slopes and decrease without bound. (C) Find the general solution of the given differenial equation y(t) Use it to determine how solutions behave as t- All solutions will increase exponentially if C> 0 and will decrease exponentially ifCs0 All solutions converge to the function yo(t) 0 The solutions are oscillatory All solutions have positive slopes, and hence increase without bound. o All solutions will increase exponentially if C s 0 and will decrease exponentially if C>0Consider the following differential equation. (A computer algebra system is recommended.) y' − 8y = 9et (a) Draw a direction field for the given differential equation.

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