Best_Mathematician
find general solution of this differential equation
dy/dx = y-2
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iambehindyou
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oh, its easily variable separable,
dy/ (y-2) =dx
did you try integrating this ?
Best_Mathematician
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no...i got confused if i need to subtract it or what
iambehindyou
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no subtract.
dy/ (y-2) =dx
got this ? can you integrate ?
Best_Mathematician
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oh ya...is the answer |dw:1364766331963:dw|
iambehindyou
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yes, now do you need to isolate 'y' also ?
if not, thats your answer.
Best_Mathematician
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ya i need to get y out
Best_Mathematician
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as i need to find c
iambehindyou
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write c as ln c'
iambehindyou
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then use log properties.
Best_Mathematician
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lets say we getta find c at x=1, y=1 how?
iambehindyou
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you are making this up ?
general solution means we need 'c'
nevertheless, y can't be 1 here.
Best_Mathematician
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|dw:1364766554143:dw|
Best_Mathematician
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ya i am making up...now lets find particular solution
iambehindyou
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y must be >=2 so that log term is defined...
iambehindyou
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ln of negative numbers are not defined in reals.
Best_Mathematician
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then we can't find c?
iambehindyou
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do we need to find 'c'?
and yes, if x=y=1, then c is complex number...
Best_Mathematician
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yes we need to find particular solution
cwrw238
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integrating gives
ln (y - 2) = x + c
so y - 2 = e^(x + c) = e^x * e*c = Ae^x
y = Ae^x + 2
iambehindyou
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oh, good....now we don't have to actually worry about c being complex..
Best_Mathematician
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no we dont its calculus
iambehindyou
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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 ?
iambehindyou
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just plug in x=1, y=1 there,and you'll get A
Best_Mathematician
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ok now the initial condition is y(0)=1
iambehindyou
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so, put x=0 y=1
this should not be any problem...
Best_Mathematician
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|dw:1364767623910:dw|
Best_Mathematician
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|dw:1364767697343:dw|
iambehindyou
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no, put e^c = A
you can keep the general form in A
and A=-2 is valid.
iambehindyou
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you have to find a constant, not specifically 'c'
A can be used, as valid constant.
Best_Mathematician
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can 1 put c1 and c2 instead....i really dont know what is A
iambehindyou
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sure, you can even put 'Best_Mathematician' instead
Best_Mathematician = -2 :P
Best_Mathematician
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ya whatever lol...so A is just a constant right
iambehindyou
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yup.
Best_Mathematician
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haha thanks...do you want going further in this equation
iambehindyou
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this is your question...do you wanna go ?
Best_Mathematician
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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.
iambehindyou
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sorry... that was latin to me :P