How many functions satisfy y''+t²y=0 with y(0)=6?

Poetria · Mar 5, 2017

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 · Mar 5, 2017

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

Poetria · Mar 5, 2017

mfb said:

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

Oh, OK. Many thanks. :)

How many functions satisfy y''+t²y=0 with y(0)=6?

Homework Statement

Discussion

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