## ksaimouli Group Title differentiate one year ago one year ago

1. ksaimouli Group Title

$\frac{ dy }{ dx }=2x-y$

2. PeterPan Group Title

@ksaimouli $\frac{dy}{dx}+y=2x$

3. ksaimouli Group Title

i tried to do this |dw:1360374033568:dw|

4. ksaimouli Group Title

$\int\limits_{}^{}dy+\int\limits_{}^{}y= \int\limits_{}^{}2x dx$

5. ksaimouli Group Title

u mean this

6. PeterPan Group Title

Can't do that, the y part has no dy in it, it won't make sense.

7. ksaimouli Group Title

so how to do this

8. PeterPan Group Title

Well, start with$\frac{dy}{dx}+y=2x$ and multiply everything by e^x

9. PeterPan Group Title

$\large e^x\frac{dy}{dx}+e^xy=2xe^x$

10. PeterPan Group Title

Now, question... what's $\large \frac{d}{dx}ye^x$ ?

11. PeterPan Group Title

$\large \frac{d}{dx}ye^x = e^x\frac{dy}{dx} + ye^{x}$

12. ksaimouli Group Title

i did not understant how did u get that ^

13. PeterPan Group Title

Implicit differentiation

14. ksaimouli Group Title

|dw:1360374611401:dw|

15. ksaimouli Group Title

hmm can u use implicit differentiation of function which is already differentiated

16. PeterPan Group Title

You can use it on any function, as far as I know :)

17. PeterPan Group Title

So, we end up with $\large \frac{d(ye^x)}{dx}=2xe^x$

18. PeterPan Group Title

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. :)

19. ksaimouli Group Title

thx

20. agent0smith Group Title

@PeterPan I haven't done these in a while, but is it incorrect to just differentiate this to: $\frac{ dy }{ dx }=2x-y$$\frac{ d^2y }{ dx^2 }=2-\frac{ dy }{ dx }$$\frac{ d^2y }{ dx^2 } + \frac{ dy }{ dx } =2$ All the original question said was: Differentiate:$\frac{ dy }{ dx }=2x-y$

21. PeterPan Group Title

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