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

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

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

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

PeterPanBest 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

PeterPanBest 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

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

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

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

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

PeterPanBest ResponseYou've already chosen the best response.2
Implicit differentiation
 one year ago

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

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

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

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

PeterPanBest 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

agent0smithBest 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

PeterPanBest 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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