General Solution of the first order differential equation

[Yr11Kid]

dy/dt + y =$$\infty$$$$\sum$$n=1Sin(nt)/n^2

 

[Goklayeh]

The equation is of the form
$$\frac{\mathrm{d}y}{\mathrm{d}t} = P(t)y(t) + Q(t)$$
with
$$P(t)\equiv -1$$ and $$Q(t):=\sum_{n\ge 1}{\frac{\sin(nt)}{n^2}}$$. So, try with the formula
$$y(t) = \exp\left(\int{P(t)\mathrm{d}t}\right)\left(\int{Q(s)\exp\left(-\int{P(s)}\mathrm{d}s\right)\mathrm{d}s})\right) \biggr|_{s=t}$$