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quation dy/dx = (x^2 + y^2)/(xy). I follow all of its steps until this step:  (v^2)/2  =  ln (x) + C. However, in the next step the example states that C = ln(k), and it follows to write the top equatoin as:  (v^2)/2  =  ln (x) + ln(k).  Where is this natural log comming from???  Thanks!

quation dy/dx = (x^2 + y^2)/(xy). I follow all of its steps until this step:  (v^2)/2  =  ln (x) + C. However, in the next step the example states that C = ln(k), and it follows to write the top equatoin as:  (v^2)/2  =  ln (x) + ln(k).  Where is this natural log comming from???  Thanks!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi,

I am looking at an example on homogeneous differential equations. I do not understand one part of this example. The example is solving the differential equation dy/dx = (x^2 + y^2)/(xy). I follow all of its steps until this step:  (v^2)/2  =  ln (x) + C. However, in the next step the example states that C = ln(k), and it follows to write the top equatoin as:  (v^2)/2  =  ln (x) + ln(k).  Where is this natural log comming from??? 
Thanks!

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