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genius12Best ResponseYou've already chosen the best response.3
are you supposed to find dy/dx?
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
im not confident of the answer in my book
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
Just rearrange. Take the 2dy to the other side, divide both sides by dx, and then divide both sides by 2.
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
can you show solution??
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
First add 2dy to both sides:\[\bf xy^3\ln(x)dx2dy=0 \implies xy^3\ln(x)dx=2dy\]Now divide both sides by dx:\[\bf xy^3\ln(x)=2\frac{dy}{dx}\]Now divide both sides by 2:\[\bf \therefore \ \frac{ xy^3\ln(x) }{ 2 }=\frac{dy}{dx}\]
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
variable seperable method?
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
@niah2411 Do you see what I did?
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
maybe my book is wrong
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
add 2dy to both sides then divide both sides by 2dx.
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
our methods are the same and also the answers, the book answer is maybe wrong
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
May be. It often happens that the publishers make a mistake in the solutions.
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
the book answer is x^2(lnx^21)+4y^2=c
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
That looks like you're supposed to find the solution to the equation, then, not just find dy/dx
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
Can you stop tagging everyone. Please don't pay attention guys.
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
@agent0smith can you give me a solution if you have one?
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
Sorry, don't really remember much of this part of calculus :(
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
@genius12 can you give me a solution using variable separable method?
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
oh..i see i understand that
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
Oh, yes you can use separation of variables: \[\Large \frac{ xy^3\ln(x) }{ 2 }=\frac{dy}{dx}\] multiply both sides by dx, divide both sides by y^3\[\Large \int\limits \frac{ x\ln(x) }{ 2 } dx= \int\limits \frac{dy}{y^3}\]Now you can integrate.
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
ohh can you give me your full solution so i can understand it really..pls?
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
Make it a little simpler to integrate:\[\Large \frac{ 1 }{ 2 } \int\limits\limits x \ln(x) dx= \int\limits\limits y^{3} dy\] On the left it looks like you'll need to use integration by parts. Sorry, I'm too tired to go through it all now, someone else can take over.
 8 months ago

niah2411Best ResponseYou've already chosen the best response.0
oh im sorry @agent0smith for the inconvenience
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
@niah2411 I'll take over from where @agent0smith left off. To continue, we will use integration by parts for the "xln(x)" integral: \[\bf \frac{ 1 }{ 2 }\int\limits_{}^{}xln(x) \ dx \implies \frac{ 1 }{ 2 } \left( \frac{x^2\ln(x)}{2}\int\limits_{}^{}\frac{ x }{ 2} \ dx \right)=\frac{ 1 }{ 2 } \left( \frac{x^2\ln(x)}{2}\frac{ x^2 }{ 4} \right)\]\[\bf =\frac{ 2x^2\ln(x)x^2 }{ 8 }+C\]Now the rightside would just be:\[\bf \int\limits_{}^{}y^{3} \ dy=\frac{y^{2}}{2}\]Now we equate the results: \[\bf \frac{1}{2y^2}=\frac{ 2x^2\ln(x)x^2 }{ 8 }+C\]
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
Can you solve for 'y' now?
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
@agent0smith You still here? Help me awaken @niah2411 ? lol
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
Hehe yeah I'm still here. After saying i was too tired, i did the int by parts on paper (i thought it would take longer than it did, or i would've just typed it up). Looks like he didn't need to find y anyway, this was the answer: x^2(lnx^21)+4y^2=c which you can get by moving terms around and multiplying by 8.
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
@agent0smith I don't know what you're saying?
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
This was the answer that he gave, from the book: x^2(lnx^21)+4y^2=c Which you can get from your result.
 8 months ago

genius12Best ResponseYou've already chosen the best response.3
According to my result, which is correct, the answer should be:\[\bf x^2(2\ln(x)1)+4y^{2}=C\]So yes, the book answer is correct and I believe he misinterpreted the meaning of "solution" or whatever. They were just looking for separation of variables and then simply bring over the x's and y's' on one side and equating it to the constant. @agent0smith
 8 months ago

agent0smithBest ResponseYou've already chosen the best response.3
Yep, that's what i worked out. The book/yours is the same.
 8 months ago
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