Second Order Equations: Solutions Construction

This lecture focuses on constructing solutions for second-order differential equations with a given second member. Starting with a known solution u₁(t), a linearly independent solution u₂(t) can be built. By combining u₁ and u₂, a solution for the equation with a second member can be obtained. The process involves finding a solution u(t) in the form of a linear combination of u₁(t) and u₂(t). The lecture covers the steps to calculate the solution and satisfy the differential equations involved. The final goal is to have a solution that satisfies the given equation with the second member. Various mathematical manipulations and integration constants are discussed throughout the lecture.