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

\( y ^ { \prime } ( t ) + 2 y + \int _ { 0 } ^ { t } y ( x ) d x \quad y ( 0 ) = 1 \)

et \( f(x)=x^{4}-6 x^{2}+1 \) on \( [-2,3] \). Which of the following is a local maximum val \( \begin{array}{llll}f \\ f\end{array} \) \( \begin{array}{llll}f(0) & \text { B. } f(\sqrt{3}) & \text { C. } f(3) & \text { D. } f(-\sqrt{3})\end{array} \)

\( y ^ { \prime } ( t ) + 2 y + \int _ { 0 } ^ { t } y ( x ) d x \quad y ( 0 ) = 1 \)

Evaluate \( \int_{0}^{\pi / 2} \frac{1}{1+\sqrt{\tan x} d x} d x \)

\( \int _ { 0 } ^ { x } 2 e ^ { - 2 t } d t = 0 \)