1. The problem statement, all variables and given/known data Can y = sin(t^2) be a solution on an interval containing t = 0 of an equation y'' + p(t)y' + q(t)y = 0 with continuous coefficients? 2. Relevant equations 3. The attempt at a solution y = sin(t^2) y' = 2tcos(t^2) y'' = 2cos(t^2) - 4t^2sin(t^2) 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.