Transform the integro-differential equations to the Laplace domain using known properties.
In the Laplace domain the equations can be solves algebraically.
Transform the solution back to the time domain.
useful properties
$$L\{ \mathrm{f} (t) \}= \mathrm{F}(s)$$
$$L\{ \mathrm{f}^\prime (t) \}=s \, \mathrm{F}(s)-\mathrm{f} (0^+)$$
$$L\left\{ \int_{0^+}^t \mathrm{f} (u) du \right\}=\frac{1}{s} \, \mathrm{F}(s)$$
Per the forum rules that you agreed to when you signed up, homework questions must be accompanied by an attempt. Be sure to include an attempt in any future homework questions you might have.
Also, if you're working on problems where you need to convert differential equations or integro-differential equations (like #1 in the two you posted), you should have access to a table of Laplace transforms. If you do a web search for "Laplace transform table" you should get lots of hits.