Solution
= Solution
Multiplication by the <integrating factor> $e^{2x}$ gives
$$
e^{2x}Ly=(e^{2x}y')'.
$$
Hence the <Sturm-Liouville problem> is
$$
\widetilde Ly=-\lambda wy,
\qquad
\boxed{\widetilde Ly=(e^{2x}y')',\quad w(x)=e^{2x}}.
$$
= Solution
Multiplication by the <integrating factor> $e^{2x}$ gives
$$
e^{2x}Ly=(e^{2x}y')'.
$$
Hence the <Sturm-Liouville problem> is
$$
\widetilde Ly=-\lambda wy,
\qquad
\boxed{\widetilde Ly=(e^{2x}y')',\quad w(x)=e^{2x}}.
$$