3 d Could any constant function yc also be a solution If so

3. (d) Could any constant function y=c     also be a solution? If so, find c.

     (e) What is the general solution of the equation?

Solution

d)

Let us substitute y=c and check

y\'=c\'=0

y\'\'=0

So, substituting y=c gives

cq(t)=0

SO q(t)=0 which is not possible

Or c=0

Hence, for y=0 we have a solution but the trivial solution

e)

We are given two solution

y1=5t^2,y2=-2t^2+tln(t)

BOth are linearly independent

So general solution is a linear combination of the two solutions

So general solution is

y=A(5t^2)+B(-2t^2+t ln(t))

y=(5A-2B)t^2+Bt ln(t)

y(t)=A\' t^2+B t ln(t)

A\' and B are arbitrary constants