GATE Mechanical 2023 | Question: 39

Question

Consider the second-order linear ordinary differential equation
$$
x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=0, \quad x \geq 1
$$
with the initial conditions
$$
y(x=1)=6,\left.\quad \frac{d y}{d x}\right|_{x=1}=2 .
$$
The value of $y$ at $x=2$ equals __________.

(Answer in integer)