# 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.

Aug 11, 2018

The functions ${y}_{1} \left(t\right) , {y}_{2} \left(t\right)$ have similar structure so substituting into the differential equation $y \left(t\right) = {t}^{\setminus \alpha}$ we have
 t^{alpha}(2alpha^2+alpha-1) = 0
and this is true for $t \setminus \ne 0$ when $\alpha = - 1 , \alpha = \setminus \frac{1}{2}$ corresponding to ${y}_{1}$ and ${y}_{2}$ hence ${y}_{1}$ and ${y}_{2}$ are a fundamental set of solutions