# Which of the Following is a solution to the differential Equation

1. Feb 9, 2013

### Northbysouth

1. The problem statement, all variables and given/known data
Which fot he following is a solution to the differential equation:

t2y" - 2ty' + 2y = 0

a)e-2tt3

b)et

c)t

d) t4

I have attached an image of the question

2. Relevant equations

3. The attempt at a solution

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?

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2. Feb 9, 2013

### Melon Knight

\neq
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.