Constructing a second solution

[physics=world]

1. Find a second solution of the differential eq. by using the formula.

xy" + y' = 0 ; y₁ = ln(x)


2.

y₂ = y₁(x) ( ∫(e^-∫P(x)dx) / (y₁(x)²) )dx





3.

I found the p(x):

p(x) = 1/x


and then I plug in everything into the formula:

y₂ = ln(x) ∫(e^{-∫((1)/(x))dx}) / (ln(x)² )dx



solve:


= ln(x) ( ∫(e^(-ln(x))) / (x)(ln(x)²))



= ∫ (1)/ (x)(ln(x))


I do not know if this is correct. I'm going to need some help.

the answer is y₂ = 1

 

[Mugged]

Hang on, if P(x) = 1/x, why did you plug in ln(x) in the exponential integral term?

Edit: Also you can't multiply ln(x) into the integral.

 

[physics=world]

Hang on, if P(x) = 1/x, why did you plug in ln(x) in the exponential integral term?

Edit: Also you can't multiply ln(x) into the integral.

sorry. typo. the ln(x) was after integration of (1/x)

 

[Mugged]

Rework the integral, i don't understand where you get that x in the denominator. An answer of y2 = 1 seems trivial..y2 could be any constant and it would satisfy the differential equation.