Question

Verify that y1(t)=t^2 and y2(t)=t^-1 are two solutions of the differential equation t^2y''-2y=0 for t>0. Then show that y=C1t^2+C2t^-1 is also a solution of this equation for any C1 and C2

Answer 1

So substitute in and show it works.

Answer 2

I don't understand.. What is it that I'm supposed to substitute in?

Answer 3

You want to show that y1 and y2 satisfy the equation
t^2y''-2y=0

So, for y1, for instance, y1 = t^2, y1' = 2t, y1'' = 2
thus
t^2y''-2y = t^2 . 2 - 2 . t^2 = 0
hence y1 is a solution.

Answer 4

Now do the same thing with y2 ...
... and then with the sum of those terms.

Answer 5

THANKS SO MUCH!

Answer 6

what about the second part?