Do the functions y_1(t)=√t and y_2(t)=1/t form a fundamental set of solutions of the equation 2t^(2)y''+3ty'-y=0,on interval 0<t<∞ ? Justify your answer.

1 Answer
Aug 11, 2018

See below.

Explanation:

The functions y_1(t), y_2(t) have similar structure so substituting into the differential equation y(t) = t^{\alpha} we have

t^{alpha}(2alpha^2+alpha-1) = 0

and this is true for t \ne 0 when alpha = -1, alpha=\frac{ 1}{2} corresponding to y_1 and y_2 hence y_1 and y_2 are a fundamental set of solutions