What is wrong here? (A differential equation)

Jamin2112
Messages
973
Reaction score
12
What is wrong here? (A differential equation)

Homework Statement



My homework has a Sturm-Louiville eigenvalue problem

Lu = u'' - u = 0, x ε (0,1)​

with u(0)=u(∏)=0. The only solution is u(x) = 0, x ε [0,1]. Right? But then other parts of this particular problem become trivial.

Homework Equations



Nothing really

The Attempt at a Solution



Plugged it into Wolfram Alpha to get u(x)=0, solved it using the characteristic equation to get u(x)=0, and also did the eigenfunction expansion to get the same answer.
 
Physics news on Phys.org


nevermind! I just saw fredholm's alternative in the lecture notes. I get it now.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top