2 questions from 2022
For \( x\in\mathbb{R} \), let the function \( y(x) \) be the solution of the differential equation \( \dfrac{dy}{dx}+12y=\cos\!\left(\dfrac{\pi}{12}x\right),\ y(0)=0 \).Then, which of the following statements is/are TRUE?
If \( y(x) \) is the solution of the differential equation \( x\,dy-(y^2-4y)\,dx=0 \) for \( x>0 \), \( y(1)=2 \), and the slope of the curve \( y=y(x) \) is never zero, then the value of \( 10y(\sqrt{2}) \) is ________.
