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.