- #1
robbondo
- 90
- 0
Homework Statement
Find the General Solution:
[tex] xy\prime + (\ln{x})y = 0 [/tex]
Homework Equations
The Attempt at a Solution
so I used the separation of variable method to get
[tex] \frac{y\prime}{y} = -\frac{\ln{x}}{x} [/tex]
Then I took the integral of both side to get
[tex] \ln{y} = -( x \ln{x} - x )( \ln{x} ) + C [/tex]
then I got rid of the ln(y) and factored out the x on the other side to get
[tex] y = ce^{-x \ln{x} ( \ln{x} - 1)} [/tex]
The back of the book tells me I should get
[tex] y = ce^{-(\ln{x})^{2}/2} [/tex]
I think what I'm having trouble with is the algebra involved in simplifying the exponent amongst other things... So how do I get what I have, to what I'm supposed to get?