The derivative of the function \( f(x)=\sqrt{x^{4}+2} \) is equal to \( f^{\prime}(x)=12 x^{2} \)

What is the solution to the differential equation \( \frac{d y}{d x}+x y=x, y(0)=-6 ? \)

What is the general solution to the following: \( \int 2 x \sin (x) d x \) ?

What is the solution to the following differential equation, subject to the initial condition \( y(0)=2 \) ? \( \frac{d y}{d x}=6 x+6 \)

Which function satisfies the differential equation \( y^{\prime \prime}=-y \)

If \( m \in \mathbb{R} \) and \( \lim _{x \rightarrow \infty} \frac{(m+5) x^{3}-x+4}{3 m x^{3}-2 x+9}=2 \), then \( m= \)