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!

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

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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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