1. A scientist is investigating the concentration of antibodies in the bloodstream of a patient following a vaccination.

The concentration of antibodies, $x$, measured in micrograms (μg) per millilitre (ml) of blood, is modelled by the differential equation

$100\frac{{d}^{2}x}{d{t}^{2}}+60\frac{dx}{dt}+13x=26$

where $t$ is the number of weeks since the vaccination was given.

Find a general solution of the differential equation.