Can y = sin(t2) be a solution on an interval containing t = 0 of an equation y + p(t) y + q(t) y = 0 with continuous coefficients? Explain your answer.

Step-by-step explanation:

y = sin(t^2)

y' = 2tcos(t^2)

y'' = 2cos(t^2) - 4t^2sin(t^2)

so the equation become

2cos(t^2) - 4t^2sin(t^2) + p(t)(2tcos(t^2)) + q(t)sin(t^2) = 0

when t=0, above eqution is 2. That is, there does not exist the solution. so y can not be a solution on I containing t=0.

Let x be the number of students in each bus.

The following equation represents the problem:

6x+7=300.

Thus, solving for x, we get

6x= 324

x=54.  is the answer