Find a general solution, in terms of Bessel functions, for the differential equation (x^{2} frac{d^{2} y}{d x^{2}}+x

Question:

Find a general solution, in terms of Bessel functions, for the differential equation $x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}-\left(1+4 x^{4}ight) y=0$ by (i) using the transformation $z=x^{2}$ and (ii) employing the inspection method for the generalized form of Bessel's equation.

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