1. The problem statement, all variables and given/known data How many functions y(t) satisfy both y''+t^2*y=0 and y(0)=6? 2. The attempt at a solution As this is a second order differential equation, two initial conditions (for y and y') would be needed to obtain a unique solution (cf. existence and uniqueness theorem). So the answer is 'infinitely many functions' as we are given only y(0)=6. Have I understood it correctly?