Differential Equation Classification

Question

anonymous · Answer

$$2t^2y''+3ty'-y=0$$

lgbasallote · Answer

by classification do you mean state the degree and order?

anonymous · Answer

$$y _{1}=t^.5$$
$$y _{2}=t ^{-1}$$

anonymous · Answer

well you need to verify that each of those functions are a solution of the given Diff. EQ

lgbasallote · Answer

if i recall right...it has something to do with substiution...right?

anonymous · Answer

ya you need to integrate then substitute i think

lgbasallote · Answer

let me try this...

$$y_1 = t^5$$
$$y' = 5t^4$$
$$y^{\prime \prime} = 20t^3$$
so if you substitute...

$$2t^2 y^{\prime \prime} + 3t y^\prime- y = 0\implies 2t^2 (20t^3) + 3t(5t^4) - t^5 = 0 \implies 40t^5 + 15t^5 - t^5 = 0\implies 54t^5 = 0$$
that doesnt sound like equal to me...

anonymous · Answer

sorry but it was supposed to be t*(1/2)

lgbasallote · Answer

lol...

lgbasallote · Answer

and the other one is still t^-1?

anonymous · Answer

yep

lgbasallote · Answer

well just follow the same thing i did. take the derivative up to the 2nd derivative then sub correspondingly. i have to go now...sadly

anonymous · Answer

haha alright thx

anonymous · Answer

i got it no need to work on it anymore