- Thread starter idontknow
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Let $y = e^{x/2}u$, then the equation becomes $u'' + (e^{4x} - 1/4)u = 0$.

Let $(1/2)e^{2x} = t$, then the equation becomes $t^2d^2u/dt^2 + tdu/dt + (t^2 - 1/4^2)u = 0$,

whch is a standard equation whose general solution is a linear combination of Bessel functions.