melmel 2 years ago answred

1. melmel

to find y any method

2. melmel

bernoulli equation or homogeneous

3. melmel

can you help me @.Sam.

4. .Sam.

$xdx + ( y -2x)dy= 0$ $xdx=-(y-2x)dy \\ -\frac{x}{y-2x}=\frac{dy}{dx}$ --------------------------------------- Try using y=vx Then $\frac{dy}{dx}=v+x\frac{dv}{dx}$

5. .Sam.

Replace the y and $$\frac{dy}{dx}$$ to v and the one given above $-\frac{x}{vx-2x}=v+x\frac{dv}{dx} \\ \frac{1}{2-v}=v+x\frac{dv}{dx}$

6. melmel

yes then?

7. melmel

the numerator can break it for the denomentor?

8. .Sam.

Then set all v into the other side $\frac{1-2v+v^2}{(2-v)x}=\frac{dv}{dx} \\ \frac{(2-v)x}{1-2v+v^2}=\frac{dx}{dv} \\ \int\limits \frac{(2-v)}{1-2v+v^2} dx=\int\limits \frac{1}{x}dx$

9. .Sam.

Should be dv $\int\limits\limits \frac{(2-v)}{1-2v+v^2} dv=\int\limits\limits \frac{1}{x}dx$

10. dumbcow

i think you get stuck here though...no way to solve for "v" the integral gives a fraction and a log

11. melmel

i think we can use here synthetic division

12. melmel

my Im right?

13. dumbcow

@melmel , no that only works if the "2-v" was in denominator

14. dumbcow
15. dumbcow

turns out you can't solve for "y" directly http://www.wolframalpha.com/input/?i=y%27%28x%29+%3D+x%2F%282x-y%28x%29%29

16. melmel

can you help me to solve and to prove that?

17. dumbcow

@.sam, already did but you cant go any further just sub in y/x for v

18. melmel

so what is my final answer?

19. dumbcow

i dunno depends on the instructions...ther is no "y =" answer

20. melmel

CAN YO HELP ME @zepdrix

21. melmel

coefficients by division?