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melmel
 one year ago
Best ResponseYou've already chosen the best response.0bernoulli equation or homogeneous

.Sam.
 one year ago
Best ResponseYou've already chosen the best response.0\[xdx + ( y 2x)dy= 0\] \[xdx=(y2x)dy \\ \frac{x}{y2x}=\frac{dy}{dx}\]  Try using y=vx Then \[\frac{dy}{dx}=v+x\frac{dv}{dx}\]

.Sam.
 one year ago
Best ResponseYou've already chosen the best response.0Replace the y and \(\frac{dy}{dx}\) to v and the one given above \[\frac{x}{vx2x}=v+x\frac{dv}{dx} \\ \frac{1}{2v}=v+x\frac{dv}{dx}\]

melmel
 one year ago
Best ResponseYou've already chosen the best response.0the numerator can break it for the denomentor?

.Sam.
 one year ago
Best ResponseYou've already chosen the best response.0Then set all v into the other side \[\frac{12v+v^2}{(2v)x}=\frac{dv}{dx} \\ \frac{(2v)x}{12v+v^2}=\frac{dx}{dv} \\ \int\limits \frac{(2v)}{12v+v^2} dx=\int\limits \frac{1}{x}dx\]

.Sam.
 one year ago
Best ResponseYou've already chosen the best response.0Should be dv \[\int\limits\limits \frac{(2v)}{12v+v^2} dv=\int\limits\limits \frac{1}{x}dx\]

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0i think you get stuck here though...no way to solve for "v" the integral gives a fraction and a log

melmel
 one year ago
Best ResponseYou've already chosen the best response.0i think we can use here synthetic division

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0@melmel , no that only works if the "2v" was in denominator

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integral+%282v%29%2F%28v%5E22v%2B1%29

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0turns out you can't solve for "y" directly http://www.wolframalpha.com/input/?i=y%27%28x%29+%3D+x%2F%282xy%28x%29%29

melmel
 one year ago
Best ResponseYou've already chosen the best response.0can you help me to solve and to prove that?

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0@.sam, already did but you cant go any further just sub in y/x for v

melmel
 one year ago
Best ResponseYou've already chosen the best response.0so what is my final answer?

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0i dunno depends on the instructions...ther is no "y =" answer

melmel
 one year ago
Best ResponseYou've already chosen the best response.0CAN YO HELP ME @zepdrix

melmel
 one year ago
Best ResponseYou've already chosen the best response.0coefficients by division?
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