# Math Help - differncial equation solve

1. ## differncial equation solve

The solution of a certain differential equation is of the form
where and are constants.
The solution has initial conditions and
Find the solution by using the initial conditions to get linear equations for and
y(t)=?

thanks!

2. Hello,

Just replace t, as you know that y(0)=4

$4=y(0)=a+b$

Then, calculate the derivative of y :

$y'(t)=4ae^{4t}+8be^{8t}$

$4=y'(0)=4a+8b \rightarrow 1=a+2b$

Then, just solve