The document contains solutions to two types of differential equations: homogeneous and linear. For the homogeneous equations, the solutions are found by representing the equations in auxiliary form to calculate the roots, then the general solution is written using the roots and arbitrary constants. For the linear equations, the solutions are found by rewriting the equations in standard form y'+P(x)y = q(x), then using an integrating factor to solve for the general solution containing an arbitrary constant.