Given constants $u,v,l$ find the solution to the differential equation $$\frac{dx}{dt}+x\left(1+\frac{v}{l}t\right)=u$$ Given that at $(0,l)$ lies on the solution. And hence find the value of $t$ when $x=0$.
I have progressed solving this equation partially. The answer included imaginary error function and other cumbersome components. As a result I am unable to find the exact value of the parameter.
You may use approximation to find the answer to the second part, but please do mention the preciseness of the answer.