Does the set {t, t int} form a fundamental set of solutions for t^2y" -- ty' +y = 0?

yes

Step-by-step explanation:

We are given that a Cauchy Euler's equation

where t is not equal to zero

We are given that two solutions of given Cauchy Euler's equation are t,t ln t

We have to find  the solutions are independent or dependent.

To find  the solutions are independent or dependent we use wronskain

If wrosnkian is not equal to zero then solutions are dependent and if wronskian is zero then the set of solution is independent.

Let

where t is not equal to zero.

Hence,the wronskian  is not equal to zero .Therefore, the set of solutions is independent.

Hence, the set {t , tln t} form a fundamental set of solutions for given equation.

if x = 1, then the answer is 3.5