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## Best_Mathematician 2 years ago find general solution of this differential equation dy/dx = y-2

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1. iambehindyou

oh, its easily variable separable, dy/ (y-2) =dx did you try integrating this ?

2. Best_Mathematician

no...i got confused if i need to subtract it or what

3. iambehindyou

no subtract. dy/ (y-2) =dx got this ? can you integrate ?

4. Best_Mathematician

oh ya...is the answer |dw:1364766331963:dw|

5. iambehindyou

yes, now do you need to isolate 'y' also ? if not, thats your answer.

6. Best_Mathematician

ya i need to get y out

7. Best_Mathematician

as i need to find c

8. iambehindyou

write c as ln c'

9. iambehindyou

then use log properties.

10. Best_Mathematician

lets say we getta find c at x=1, y=1 how?

11. iambehindyou

you are making this up ? general solution means we need 'c' nevertheless, y can't be 1 here.

12. Best_Mathematician

|dw:1364766554143:dw|

13. Best_Mathematician

ya i am making up...now lets find particular solution

14. iambehindyou

y must be >=2 so that log term is defined...

15. Best_Mathematician

no it is not

16. Best_Mathematician

it is 1 and 1

17. iambehindyou

ln of negative numbers are not defined in reals.

18. Best_Mathematician

then we can't find c?

19. iambehindyou

do we need to find 'c'? and yes, if x=y=1, then c is complex number...

20. Best_Mathematician

yes we need to find particular solution

21. Best_Mathematician

at y(1) = 1

22. cwrw238

integrating gives ln (y - 2) = x + c so y - 2 = e^(x + c) = e^x * e*c = Ae^x y = Ae^x + 2

23. iambehindyou

oh, good....now we don't have to actually worry about c being complex..

24. Best_Mathematician

whats Ae^x

25. Best_Mathematician

no we dont its calculus

26. iambehindyou

you didn't get this ? : ln (y - 2) = x + c so y - 2 = e^(x + c) = e^x * e*c = Ae^x y = Ae^x + 2 what you have doubt with ?

27. iambehindyou

just plug in x=1, y=1 there,and you'll get A

28. Best_Mathematician

ok now the initial condition is y(0)=1

29. iambehindyou

so, put x=0 y=1 this should not be any problem...

30. Best_Mathematician

|dw:1364767623910:dw|

31. Best_Mathematician

|dw:1364767697343:dw|

32. iambehindyou

no, put e^c = A you can keep the general form in A and A=-2 is valid.

33. iambehindyou

you have to find a constant, not specifically 'c' A can be used, as valid constant.

34. Best_Mathematician

can 1 put c1 and c2 instead....i really dont know what is A

35. iambehindyou

sure, you can even put 'Best_Mathematician' instead Best_Mathematician = -2 :P

36. Best_Mathematician

ya whatever lol...so A is just a constant right

37. iambehindyou

yup.

38. Best_Mathematician

haha thanks...do you want going further in this equation

39. iambehindyou

this is your question...do you wanna go ?

40. Best_Mathematician

ya lol..... Use a technological tool and Euler's method with ten steps of size 0.1 to estimate y(1). Make certain to include supporting screen captures.

41. iambehindyou

sorry... that was latin to me :P

42. Best_Mathematician

ok

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