Cauchy-Euler

The function $y(t)$ satisfies $$ t^2 y^{\prime \prime}(t)-2 t y^{\prime}(t)+2 y(t)=0 $$ where $y^{\prime}(t)$ and $y^{\prime \prime}(t)$ denote the first and second derivatives of...

Consider the homogeneous ordinary differential equation $x^2 \frac{d^2y}{dx^2} - 3x \frac{dy}{dx} + 3y = 0$, $x > 0$ with $y(x)$ as a general solution. Given that $y(1) = 1$ and $y...