## ksaimouli 2 years ago differentiate

1. ksaimouli

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

2. PeterPan

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

3. ksaimouli

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

4. ksaimouli

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

5. ksaimouli

u mean this

6. PeterPan

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

7. ksaimouli

so how to do this

8. PeterPan

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

9. PeterPan

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

10. PeterPan

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

11. PeterPan

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

12. ksaimouli

i did not understant how did u get that ^

13. PeterPan

Implicit differentiation

14. ksaimouli

|dw:1360374611401:dw|

15. ksaimouli

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

16. PeterPan

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

17. PeterPan

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

18. PeterPan

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

thx

20. agent0smith

@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

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