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anonymous
 one year ago
can anyone help me how to solve this homogenous equation please: [x csc (y/x)  y] dx + x dy = 0 ..its says here that the answer should be ln l x/c l = cos (y/x)
anonymous
 one year ago
can anyone help me how to solve this homogenous equation please: [x csc (y/x)  y] dx + x dy = 0 ..its says here that the answer should be ln l x/c l = cos (y/x)

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amoodarya
 one year ago
Best ResponseYou've already chosen the best response.3take \[\frac{y}{x}=v\\y=vx\\y'=v+xv'\\(xcsc(\frac{y}{x})y)dx+xdy=0\\(xcsc(\frac{y}{x})y)+x\frac{dy}{dx}=0\\ divx\\(\csc(\frac{y}{x})\frac{y}{x})+y'=0\\\]

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.3if you put v it will be simple to solve can you go on ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0this is substitution method for first order odes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i'll try :) our prof didn't really explained it to us very well the steps in solving it

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0usually you have to do substitution and then argh I forgot... a. I didn't have trig involved for my odes b. substitution was my least favorite.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actually i have already taken up integral and differential calculus but this is my first time encountering this topic

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0I really didn't like this method at all when I came across it x(

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0my favorites are integrating factor and exact oh yeah!

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.3\[(\csc(v)v)+(v+v'x)=0\\csc(v)+xv'=0\\xv'=\csc(v)\\x\frac{dv}{dx}=\frac{1}{\sin(v)}\\\sin(v)dv=\frac{dx}{x}\\\] now apply integral both sides

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0oh there it is the dv/dx has to be on the left and eventually that nasty problem turns into a simple separation of variables.

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.3it is one step to solve it completely!

SolomonZelman
 10 months ago
Best ResponseYou've already chosen the best response.0\(\color{#000000 }{ \displaystyle \sin(v){\tiny~~}dv=\frac{dx}{x} }\) and you integrate both sides... Just go, "magic", Blah Blah Blah?\ \(\color{#000000 }{ \displaystyle \color{red}{\int}\sin(v){\tiny~~}dv=\color{red}{\int}\frac{dx}{x} }\) \(\tt Or,{\tiny~~~}are{\tiny~~~}you{\tiny~~~}integrating{\tiny~~~}with{\tiny~~~}respect{\tiny~~~}to{\tiny~~~}a{\tiny~~~}variable?\) Maybe something like this?\(\tiny\\[0.8em]\) \(\color{#000000 }{ \displaystyle \sin(v){\tiny~~}dv=\frac{dx}{x} }\)\(\tiny\\[1.4em]\) \(\color{#000000 }{ \displaystyle \sin(v){\tiny~~}\frac{dv}{dx}=\frac{1}{x} }\) and then, pam parara! \(\color{#000000 }{ \displaystyle \color{red}{\int}\sin(v){\tiny~~}\frac{dv}{dx}\color{red}{dx}=\color{red}{\int}\frac{1}{x}\color{red}{dx} }\) I am just asking... Found this thread, but I know that this is a little wierd that I am replying to a 5monthold thread.

UsukiDoll
 10 months ago
Best ResponseYou've already chosen the best response.0yeahhhh....I don't understand how some users have the desire to post comments on an old thread but the first comment is the correct way of doing the problem. first substitution and then towards the end it becomes a simple (or hopefully...not that complex) separation of variables.
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