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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: bubbles on August 06, 2008, 05:36:59 pm

Title: The solutions of differential equation dy/dx = f(y)
Post by: bubbles on August 06, 2008, 05:36:59 pm: (http://i50.photobucket.com/albums/f313/mang0es/f.jpg)
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: Mao on August 06, 2008, 06:15:27 pm: $x=\int \frac{1}{f(y)}\; dy$ ?
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: bubbles on August 06, 2008, 06:29:15 pm: Quote from: Mao on August 06, 2008, 06:15:27 pm
$x=\int \frac{1}{f(y)}\; dy$ ?

?? I did that didn't I?
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: Mao on August 06, 2008, 06:30:50 pm: i can't see it :P photo is moved or deleted?
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: ed_saifa on August 06, 2008, 06:33:03 pm: Maybe because when they integrated it, they made it into an inverse cos instead of an inverse sine?
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: Mao on August 06, 2008, 06:34:44 pm: Quote from: ed_saifa on August 06, 2008, 06:33:03 pm
Maybe because when they integrated it, they made it into an inverse cos instead of an inverse sine?

what can you see it?!
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: ed_saifa on August 06, 2008, 06:37:04 pm: Quote from: Mao on August 06, 2008, 06:34:44 pm
Quote from: ed_saifa on August 06, 2008, 06:33:03 pm
Maybe because when they integrated it, they made it into an inverse cos instead of an inverse sine?

what can you see it?!
Nope. I saw it before :P
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: bubbles on August 06, 2008, 06:46:28 pm: oh sorry >< my bad
(http://i50.photobucket.com/albums/f313/mang0es/f.jpg)
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: bubbles on August 06, 2008, 06:49:25 pm: Quote from: ed_saifa on August 06, 2008, 06:33:03 pm
Maybe because when they integrated it, they made it into an inverse cos instead of an inverse sine?

Yeah maybe the answer at the back (Essentials) is wrong, just wanted to make sure ;D
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: bubbles on August 06, 2008, 06:50:40 pm: Another question:

(http://i50.photobucket.com/albums/f313/mang0es/g.jpg)
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: Mao on August 06, 2008, 06:57:42 pm: Bubbles: question 1:

the two expressions are equivalent:

$\sin\left(x+\frac{\pi}{2}\right)=\cos(x)$ (think graphically: translating the sin graph one quadrant to the left, you get cos!)
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: Mao on August 06, 2008, 07:02:45 pm: $\frac{dy}{dx}=9-y^2,\; y(7/6)=0$

$\implies x=\frac{1}{6}\int \frac{1}{3+y}+\frac{1}{3-y}\; dy$

$\implies 6x=log_e|3+y|-log_e|3-y|+c$ (this is the step you went wrong. forgot the minus in front of the ln(3-y)

$c=7$

$\implies 6x-7 = log_e \left| \frac{3+y}{3-y}\right|$

$\implies e^{6x-7} = -1 - \frac{6}{y-3}$

$\implies -e^{6x-7}-1=\frac{6}{y-3}$

$\implies y=-\frac{6}{e^{6x-7}+1}+3$

$\implies y=\frac{3e^{6x-7}+3-6}{e^{6x-7}+1}$

$\implies y=\frac{3(e^{6x-7}-1)}{e^{6x-7}+1}$
Title: Re: The solutions of differential equation dy/dx = f(y)
Post by: bubbles on August 06, 2008, 07:15:32 pm: THANKS MAO!!!