Finding Solutions for Second Order ODE with Initial Condition y(0)=6

[Poetria]

Homework Statement

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?

 

[mfb]

As long as all those different y'(0) lead to valid solutions, that works.

 

[Poetria]

As long as all those different y'(0) lead to valid solutions, that works.

Oh, OK. Many thanks. :)