How to solve the following differential equation $B'(t)=1100\exp({\frac{\ln{0.5}}{5}t})+\frac{\ln{0.5}}{6}B(t)$?

Question

I have constructed this differential equation $B'(t)=1100\exp\left(\frac{\ln{0.5}}{5}t\right)+\frac{\ln{0.5}}{6}B(t)$

I have constructed this equation when i asked this question here, but i'm unable to solve this equation from methods that i know.

I'm unable to separate it, and it's not of the form $y'+p(t)y=q(t)$.

What should be done here?

Answer 1

The equation is of type $y'+p(t)y=q(t)$.

The solution for $B(t)$ will be $B(t)=\frac{\int{\mu(t)q(t)dt +c}}{\mu(t)}$,$\mu(t)=e^{\int{}p(t)dt}$.