New solutions in linearized R+R2 gravity

A general method is proposed to solve in the linear approximation the fourth-order gravitational equations, which stem from Lagrangians $ \text{Q} = 1 ‐ g\left( {R + \frac{1}{2}aR^2 + bR_{av} R^{av} } \right) ‐ x\text{Q}. $ The metric of a static spherically symmetric body and the metric of a straight infinitely thin cosmic string are given.