Second order homogenous differential equation

Question

Assignment:

Show that y₁=(t) and y₂(t)=1/t are solutions of

t²y" + ty' - y = 0

Determine the following solutions of this equation, or explain why none exist.

• The solution y = y(t) satisfying y(1)=0, y'(1)=2
• All solutions satisfying lim_t→0 + y(t)=0 as t approaches zero
• All solutions satisfying lim_t→∞ (t)=0 as t approaches infinity.

Provide complete and step by step solution fo_{r the question and sh}ow calculations and use formulas.