ATAR Notes: Forum

VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: Mao on May 11, 2011, 06:54:24 pm

Title: Mao's maths thread
Post by: Mao on May 11, 2011, 06:54:24 pm: Thought I might put up a thread of my own for my stupid problems. Calculus related. Please help if you can!
Title: Re: Mao's maths thread
Post by: Thu Thu Train on May 11, 2011, 06:57:48 pm: $\int e^x = f_u(n)$
Title: Re: Mao's maths thread
Post by: Mao on May 11, 2011, 06:58:49 pm: Today I was solving the non-linear ODE:

$\frac{d^2 c}{dx^2} - c^2 = -1$

I got the Weierstrass P function as the answer:

$c=6^{1/3} WeierstrassP\left[ z= \frac{x + C[1]}{6^{1/3}}; \omega_1=2 \cdot 6^{1/3}, \omega_2=C[2]} \right]$ , where C[1] and C[2] are the constants of integration.

It is fairly obvious that there is a constant-value solution $c= 1$ . However, I cannot work out what values of C[1] and C[2] will give me this constant-value solution. Anyone?
Title: Re: Mao's maths thread
Post by: humph on May 14, 2011, 12:02:18 am: The Weierstrass function always has a singularity (a double pole at the origin, when viewed as a complex-valued function), so it's impossible to choose such constants C[1], C[2]. Look up the wikipedia page on Weierstrass functions and you'll see that they can be defined as a solution to a particular nonlinear ODE, but again there is a constant solution to this ODE (so the solution is not unique).
Title: Re: Mao's maths thread
Post by: Mao on May 14, 2011, 01:24:11 pm: Quote from: humph on May 14, 2011, 12:02:18 am
The Weierstrass function always has a singularity (a double pole at the origin, when viewed as a complex-valued function), so it's impossible to choose such constants C[1], C[2]. Look up the wikipedia page on Weierstrass functions and you'll see that they can be defined as a solution to a particular nonlinear ODE, but again there is a constant solution to this ODE (so the solution is not unique).

Thank you humph. I guess this will be the last time I trust Mathematica to give me the complete solution :P