List of top Ordinary Differential Equations Questions on Cauchy’s and Euler’s Equations

Let \( y(x) \) be the solution of the following initial value problem \[ x^2 \frac{d^2y}{dx^2} - 4x \frac{dy}{dx} + 6y = 0, x > 0, \] \[ y(2) = 0, \frac{dy}{dx}(2) = 4. \] Then \( y(4) = \(\underline{\hspace{1cm}}\) \).