Answer
The order is 2.
The differential equation is linear.
Work Step by Step
The differential equation $$t^2\frac{d^2y}{dt^2} +t\frac{dy}{dt}+2y=\sin t $$ has order 2 because the second derivative $\frac{d^2y}{dt^2}$ is the highest derivative in the equation.
To see it is linear, we subtract $\sin t$ from both sides to get $$t^2\frac{d^2y}{dt^2} +t\frac{dy}{dt}+2y-\sin t=0.$$ Since the left hand side is a linear function of $y$ and its derivatives, our differential equation is linear.
