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ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ dy }{ dx }=2xy\]
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
@ksaimouli \[\frac{dy}{dx}+y=2x\]
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
i tried to do this dw:1360374033568:dw
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits_{}^{}dy+\int\limits_{}^{}y= \int\limits_{}^{}2x dx\]
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
u mean this
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
Can't do that, the y part has no dy in it, it won't make sense.
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
so how to do this
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
Well, start with\[\frac{dy}{dx}+y=2x\] and multiply everything by e^x
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
\[\large e^x\frac{dy}{dx}+e^xy=2xe^x\]
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
Now, question... what's \[\large \frac{d}{dx}ye^x\] ?
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
\[\large \frac{d}{dx}ye^x = e^x\frac{dy}{dx} + ye^{x}\]
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
i did not understant how did u get that ^
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
Implicit differentiation
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
dw:1360374611401:dw
 one year ago

ksaimouli Group TitleBest ResponseYou've already chosen the best response.0
hmm can u use implicit differentiation of function which is already differentiated
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
You can use it on any function, as far as I know :)
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
So, we end up with \[\large \frac{d(ye^x)}{dx}=2xe^x \]
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
so, just bring the dx on the other side... \[\large d(ye^x)=2xe^xdx\] And integrate both sides... \[\large ye^x = \int\limits_{}^{}2xe^x dx\] And you're good to go. :)
 one year ago

agent0smith Group TitleBest ResponseYou've already chosen the best response.0
@PeterPan I haven't done these in a while, but is it incorrect to just differentiate this to: \[\frac{ dy }{ dx }=2xy\]\[\frac{ d^2y }{ dx^2 }=2\frac{ dy }{ dx }\]\[\frac{ d^2y }{ dx^2 } + \frac{ dy }{ dx } =2\] All the original question said was: Differentiate:\[\frac{ dy }{ dx }=2xy\]
 one year ago

PeterPan Group TitleBest ResponseYou've already chosen the best response.2
I was wondering about that, but then again, ksaimouli put in "I tried to do this", with a drawing that shows an attempt to solve it as a differential equation, so.... yeah
 one year ago
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