$($ii$)$ The DE $y^{\text{'}\text{'}\text{'}}-cos(t)(y^{\text{'}\text{'}}+2y)+tan((y^{\text{'}}{)}^4)-t=0,$ is equivalent to

$($A$)x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=x_3$

$x_3^{\text{'}}=cos(t)(x_3+2x_1)-tan(x_2^4)+t$

$($B$)x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=x_3$

$x_3^{\text{'}}=-cos(t)(x_3+2x_1)+tan(x_2^4)-t$

$($C$)x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=x_3$

$x_3^{\text{'}}=cos(x_3+2x_1)-tan(x_2^4)+t$

$($D$)x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=x_3$

$x_3^{\text{'}}=cos(t)(x_1+2x_3)-tan(x_2^4)+t$