Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by

$$ f(x)= \begin{cases}x^2-4 x-5 & \text { if } x \geq 1, \\ 2 x & \text { if } x<1 .\end{cases} $$

Which one of the following statements is TRUE?

Which one of the following is the solution of the differential equation

$$ x^2 \frac{d y}{d x}+9 x y=x^4(\text { for } x>0) $$

given that $y=0$ when $x=1$ ?

What is the value of $\int_0^\pi x|\cos x| \sin x d x$ ?

Consider an elastic collision between two particles $A$ and $B$ of same mass, moving in the same direction. Particle $A$ is moving at speed $v_A$ and particle $B$ is moving at speed $v_B$. In the figures shown, the solid lines represent the motion before the collision and the dotted lines represent the motion after the collision. Which of the following describes the motion of these two particles most accurately?