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ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ dx }=2xy\]

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

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0i tried to do this dw:1360374033568:dw

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

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

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

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

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

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

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0i did not understant how did u get that ^

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.2Implicit differentiation

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1360374611401:dw

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0hmm can u use implicit differentiation of function which is already differentiated

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

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

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.2so, 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. :)

agent0smith
 2 years ago
Best 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:\[\frac{ dy }{ dx }=2xy\]

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.2I 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
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