Looks like the equation is

Differentiating both sides yields the linear ODE,

or

Multiply both sides by the integrating factor  :
:


Integrate both sides, then solve for  :
:


The given answer choices all seem to be missing <em>C</em>, so I suspect you left out an initial condition. But we can find one; let  , then the integral vanishes and we're left with
, then the integral vanishes and we're left with  . So
. So

So the particular solution is
