Transform the given equation

$u^{\text{'}\text{'}}5\mathrm{.}5u4u=10sint$

into a system of first order equations.

$x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=10s{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}-8x_1-5\mathrm{.}5x_2$

$x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=10s{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}4x_{1}5\mathrm{.}5x_2$

$x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=10$ sint $-5\mathrm{.}5x_1-4x_2$

$x_1^1=x_2$

$x_2^{\text{'}}=10sint-4x_1-5\mathrm{.}5x_2$

$x_1^{\text{'}}=x_2$

$x_3^{\text{'}}=10s{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}5\mathrm{.}5x_{1}4x_2$