(2) \( \frac{d y}{d x}-2 x y=x e^{x^{2}} \)

Find the point(s) at which the function \( f(x)=10-|x| \) equals its average value on the interval \( [-10,10] \) The function equals its average value at \( x=\square \) (Type an integer or a fraction. Use a comma to separate answers as needed.)

\( \int _ { - 1 } ^ { 1 } \frac { x \cos ^ { 2 } x } { 1 + x ^ { 2 } } d x \)

Given the following velocity function of an object moving aiong a line, find the position function with the given initial position. \[ v(t)=2 \sqrt[3]{t}, s(0)=3 \] The position function is \( s(t)=\square \)

Given the following velocity function of an object moving along a line, find the position function with the given initial position.

Resuelve la ecuación diferencial \( \frac{dy}{dx} = 3y^{2} \) dado que \( y(0) = 1 \).