Question

Which of the following pairs of values of A and B are such that all solutions of the differential equation dy/dt = =Ay+B diverge away from the line y=9 as t→[infinity] ? Select all that apply a.A=−2,B=−18

b.A=−1,B=9
c.A=1,B=−9
d.A=2,B=−18
e.A=2,B=18
f.A=3,B=−27
g.A=9,B=−1
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Answer 1

To determine which pairs of values of A and B result in all solutions of the differential equation dy/dt = Ay + B diverging away from the line y = 9 as t approaches infinity, analyze the behavior of the solutions. Pairs of values that satisfy this condition are A = -2, B = -18 and A = 1, B = -9.

Step-by-step explanation:

To determine which pairs of values of A and B result in all solutions of the differential equation dy/dt = Ay + B diverging away from the line y = 9 as t approaches infinity, we can analyze the behavior of the solutions.

The differential equation represents the rate of change of y with respect to t, and in order for the solutions to diverge away from the line y = 9, the coefficient A must be negative. This ensures that the solutions move away from the line instead of approaching it.

From the given options, the pairs of values that satisfy this condition are:

• A = -2, B = -18
• A = 1, B = -9