Is My Solution to the Reduction of Order Problem Correct?

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I think I have this right, its just its an online assignment and I don't want to lose any points on it.(1/4 my grade)

Question: Find y2 if y1= x^(-1) and the equation: x^2y"+3ty'+y=0.

I solved(using Abel's) for it:
ln(x)/x

but I am not entirely sure.

Wondering if I am spot on or am not doing it right/ thanks
 
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bigt9 said:
I think I have this right, its just its an online assignment and I don't want to lose any points on it.(1/4 my grade)

Question: Find y2 if y1= x^(-1) and the equation: x^2y"+3ty'+y=0.

I solved(using Abel's) for it:
ln(x)/x

but I am not entirely sure.

Wondering if I am spot on or am not doing it right/ thanks

Welcome to the PF.

Can you please show the steps you used to arrive at that solution?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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