Which of the Following is a solution to the differential Equation

[Northbysouth]

Homework Statement

Which fot he following is a solution to the differential equation:

t²y" - 2ty' + 2y = 0

a)e^-2tt³

b)e^t

c)t

d) t⁴

I have attached an image of the question

Homework Equations

The Attempt at a Solution

I tried answer d first:

y = t⁴

y' = 4t₃

y" = 12t²

Plugging in these derivatives:

t²(12t²) - 2t(4t³) + 2(t⁴) = 0

I also checked with y = t and this solution works as well. So how do I distinguish between which one is the correct answer?

 

[Melon Knight]

\neq

t²(12t²) - 2t(4t³) + 2(t⁴) = 0

I also checked with y = t and this solution works as well. So how do I distinguish between which one is the correct answer?

I think you just made an arithmetic mistake ;)
$$t^2(12t^2) - 2t(4t^3) + 2(t^4) = 12t^4 - 8t^4 + 2t^4 = 6t^4 \neq 0$$

In many cases, DE's can have multiple different solutions.