Question

Please help me with the following thermo question from the picture and below continuation

Consider the following differential equation. (A computer algebra system is recommended.) 7t (a) Draw a direction field for the given differential equation. 1.5 10

(b) Based on an inspection of the direction field, describe how solutions behave for large t.

All solutions seem to eventually have negative slopes, and hence decrease without bound.All solutions seem to eventually have positive slopes, and hence increase without bound.    The solutions appear to be oscillatory.If y(0) > 0, solutions appear to eventually have positive slopes, and hence increase without bound. If y(0) ≤ 0, solutions appear to have negative slopes and decrease without bound.All solutions seem to approach a line in the region where the negative and positive slopes meet each other.

(c) Find the general solution of the given differential equation.

y(t) =

Use it to determine how solutions behave as

t → ∞.

All solutions converge to the function y =

t

8

−

1

64

.

All solutions will decrease exponentially.

    

All solutions will increase exponentially.

All solutions converge to the function y = −

t

8

−

1

64

.All solutions converge to the function y =

t

7

−

1

64

.

Answer 1

8? 8 b 1. 69 8 6 왕e Cs