The solution of a certain differential equation is of the form $\displaystyle {y}{\left({t}\right)}={a}{e}^{{{2}{t}}}+{b}{e}^{{{3}{t}}}$, where $\displaystyle {a}$ and $\displaystyle {b}$ are constants.

The solution has initial conditions $\displaystyle {y}{\left({0}\right)}={5}$ and $\displaystyle {y}'{\left({0}\right)}={2}.$

Find the solution by using the initial conditions to get linear equations for $\displaystyle {a}$ and $\displaystyle {b}.$

$\displaystyle {y}{\left({t}\right)}=$ Preview Question 6