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June 3rd, 2012, 03:32 PM   #11
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Re: differential equation use substitution methode

Quote:
 Originally Posted by zell^ thx problems solved. now got an other one problem. how do i found out C is just C not lnC? how can i recognize it after intergration? example: $\int \frac{1}{y}dy=\int \frac{1}{x}dx$ $ln y= ln x+ ln C$ other one $\int \frac{1}{y}=\int \frac{1}{x^{2}}dx$ $ln y=-\frac{1}{x}+ln C$ confused
It doesn't matter. For any (positive) C, ln(C) is just some real number. It doesn't matter whether you call the constant "ln(C)" or "C".

 June 3rd, 2012, 10:56 PM #12 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: differential equation use substitution methode We know C is arbitrary. And ln C is as arbitrary as C. So, without any loss of genarelity, we can say that C==ln C :)

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