# Constructing a second solution

1. Mar 22, 2014

### 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

Last edited: Mar 22, 2014
2. Mar 22, 2014

### Mugged

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

Edit: Also you cant multiply ln(x) into the integral.

Last edited: Mar 22, 2014
3. Mar 22, 2014

### physics=world

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

4. Mar 22, 2014

### Mugged

Rework the integral, i dont 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.