Consider the following differential equation. (A computer algebra system is reco

Question

Consider the following differential equation. (A computer algebra system is recommended.) y' - 7y = 8e Draw a direction field for the given differential equation. Based on an inspection of the direction field, describe how solutions behave for large t. All solutions seem to converge to the function y_0(t) = 0. The solutions appear to be oscillatory. If y(0) 4/3 solutions have negative slopes and decrease without bound. All solutions seem to eventually have positive slopes, and hence increase without bound. solutions eventually have positive slopes, and hence increase without bound. If y(0) If y(0) > -4/3, , solutions have negative slopes and decrease without bound. Find the general solution of the given differential equation. Use it to determine how solutions behave as t rightarrow infinity.

Explanation / Answer

solution is

y(t) = e^7t (-4/3 e^{-6t} + C) as the equation is d(ye^-7t)/dt = 8e^{-6t}

for b it is the last option

for c it is the third option

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