Is My Solution to the Reduction of Order Problem Correct?

[bigt9]

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

 

[berkeman]

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?