Question

y"=0

Answer 1

\[y''=0,\qquad y'(0)=v_0, \qquad y(0)=y_0\]
\[\begin{align}\frac{\mathrm d^2y}{\mathrm dx^2} &= 0\\
\int\frac{\mathrm d^2y}{\mathrm dx^2} \mathrm dx&= \int(0)\,\mathrm dx\\
\frac{\mathrm dy}{\mathrm dx}&=v_0\\\int\frac{\mathrm dy}{\mathrm dx}\mathrm dx&=\int v_0\,\mathrm dx\\
\\y(x)&=v_0x+y_0\end{align}\]