$ay(0\mathrm{.}6),$ where $y(x)is$ the solution $of$ the initial$-$value problem $y^{\text{'}}=2cos(x+y),y(0)=0.(Round$ your final answer $to$ four decimal places.$)$

$(b)$ Use Euler's method with step size $0\mathrm{.}1to$ estimate $y(0\mathrm{.}6),$ where $y(x)is$ the solution $of$ the initial$-$value problem $y^{\text{'}}=2cos(x+y),y(0)=0.(Round$ your final answer $to$ four decimal places.$)$