# Todai Entrance Exam: Math 2017 – Problem 2

**(1)**

**(2)**

Let and . So, thanks to the given fact:

**(3)**

We solve the characteristic equation of the above homogenous second order linear differential equations:

So:

If :

which is the excluded solution.

If :

Note that if in this case then , which is the excluded solution.

If then , so , .

**(4)**

How to find so that:

?

Also notice that: