homogeneous differential equation problem

Thread Starter

PG1995

Joined Apr 15, 2011
816
Update: I have solved Q1. Thanks for giving it a look. If someone is in process of writing a reply, then I still genuinely thank you.
 

steveb

Joined Jul 3, 2008
2,436
Update: I have solved Q1. Thanks for giving it a look. If someone is in process of writing a reply, then I still genuinely thank you.
It looks like you figured out that Q1 is answered by considering that the dx term you thought was missing was simply moved over to the other term.

For Q2, one simply has to use the log properties that adding logarithms is like multiplying the arguments and subtracting is like dividing. From this, multiplication by 2 on the log is like a power of two on the argument. I would write it out in TeX, but it's a little tedious, so I'll just sketch it out.

y/x=2 log|1+y/x|+log|x|-log|c|

y/x=log|(1+y/x)^2|+log|x|-log|c|

y/x=log|(x(1+y/x)^2)/c|

y/x=log|(x^2(1+y/x)^2)/(cx)|

y/x=log|(x+y)^2)/(cx)|
 
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