- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks again to those who participated in last week's POTW! Here's this week's problem!
-----
Problem: Consider a differential equation of the form
\[A(x)y^{\prime\prime} + B(x)y^{\prime} + C(x)y + \lambda D(x)y = 0.\]
Show that you can express this equation in Sturm-Liouville form, given by
\[\frac{d}{dx}\left[p(x)\frac{dy}{dx}\right] - q(x)y -\lambda r(x)y = 0.\]
-----
Hint:
Remember to read the POTW submission guidelines to find out how to submit your answers!
-----
Problem: Consider a differential equation of the form
\[A(x)y^{\prime\prime} + B(x)y^{\prime} + C(x)y + \lambda D(x)y = 0.\]
Show that you can express this equation in Sturm-Liouville form, given by
\[\frac{d}{dx}\left[p(x)\frac{dy}{dx}\right] - q(x)y -\lambda r(x)y = 0.\]
-----
Hint:
First divide every term by $A(x)$ and then multiply the equation by $\exp\left(\displaystyle \int\frac{B(x)}{A(x)}\,dx\right)$.
Remember to read the POTW submission guidelines to find out how to submit your answers!