$\mathrm{dsys} ≔ \left\{\frac{{\ⅆ}^2}{\ⅆ t^2} y\left(t\right) \+ y\left(t-\frac{1}{10}\right)\=0\, y\left(0\right)\=1\, y\'\left(0\right)\=0\right\}$

$\mathrm{dsys}:=\left\{\frac{{\ⅆ}^2}{\ⅆt^2}y\left(t\right)\+y\left(t-\frac{1}{10}\right)\=0\,y\left(0\right)\=1\,\mathrm{D}\left(y\right)\left(0\right)\=0\right\}$

$\mathrm{dsn} ≔ \mathrm{dsolve}\left(\mathrm{dsys}\, \mathrm{numeric}\right)\:$

$\mathrm{plots}\:-\mathrm{odeplot}\left(\mathrm{dsn}\,0..10\,\mathrm{size}\=\left[600\,''golden''\right]\right)\;$

$\mathrm{dsys\_var} ≔ \left\{\frac{\ⅆ}{\ⅆ t} x\left(t\right) \= -x\left(t-\frac{1}{2}-\frac{\exp \left(-t\right)}{2}\right)\, x\left(0\right)\=1\right\}$

$\mathrm{dsys\_var}:=\left\{\frac{\ⅆ}{\ⅆt}x\left(t\right)\=-x\left(t-\frac{1}{2}-\frac{1}{2}{\ⅇ}^{-t}\right)\,x\left(0\right)\=1\right\}$

$\mathrm{max\_delay} ≔ \mathrm{fsolve}\left(t \= \frac{1}{2}\+\frac{\exp \left(-t\right)}{2}\, t\right)\;$

$\mathrm{max\_delay}:=0.7388350311$

$\mathrm{dsn\_var} ≔ \mathrm{dsolve}\left(\mathrm{dsys\_var}\, \mathrm{numeric}\, \mathrm{delaymax}\=0.74\right)\:$

$\mathrm{plots}:-\mathrm{odeplot}\left(\mathrm{dsn\_var}\, 0..5\,\mathrm{size}\=\left[600\,''golden''\right]\right)$