Hi,
I'm studying for my final exam at the moment and i found this question from the past exam paper. but i have no idea how to solve it.
can anyone please please help me!!!
thanks!!!!!!
Make the change of variable $\displaystyle y'=y/x^{\alpha}$ and rewrite the de in terms of $\displaystyle y'$ and $\displaystyle x$. Then put $\displaystyle x'=\beta x^{\gamma}$ and you should find that $\displaystyle x'$ and $\displaystyle y'$ satisfy the Bessel equation of order $\displaystyle n$.
RonL
You do know that the ' do not denote differentiation here don't you?
Try instead $\displaystyle u(x)=y(x)/x^{\alpha}$ first, from this compute $\displaystyle \frac{dy}{dx}$ and $\displaystyle \frac{d^2y}{dx^2}$ in terms of $\displaystyle x$, $\displaystyle u$, $\displaystyle \frac{du}{dx}$ and $\displaystyle \frac{d^2u}{dx^2}$ and substitute into the DE.
RonL