DOI: https://doi.org/10.36347/sjpms.2026.v13i03.005

Pages: 133-139

The importance of teaching linear differential equations is demonstrated by the fact that all scientific and technical phenomena are differential equations that are expressed and described in the mathematical sciences. Modern comparative mathematics, which contains several papers pertaining to population growth, engineering, economics, natural science, and technological issues, is fundamentally based on differential equations. A wide range of physics topics are also covered, such as heat, mechanics, atoms, electronics, magnetism, light, and waves. This article examines the theory of eigenvalues and eigenfunctions with boundary conditions in fourth-order linear inhomogeneous differential equations with coefficients of constant and boundary conditions. A boundary value problem in differential equations is characterized as a boundary value problem with a number of extra constraints. Applying the given constraints to the answer of the boundary value problem allows one to solve the differential equation with the given constraints. The boundary value matter's conditions are actually met by this. Initial value problems and differential equation problems with boundary conditions are comparable. For a system of equations, the initial value problem is the condition that has the value of the independent variable. An independent variable in the equation is specified in a boundary value problem with conditions on the boundaries, and the initial value is the data value that matches the minimum or maximum input, internal, or output value specified. This work aims to address the problem of eigenvalues and eigenfunctions with boundary conditions. When the fourth order differential equations border of the boundary values in the solution are reached D1, D2, D3, and D4 are determined, the boundary problem is the inability to obtain the constants. We resolve this matter by taking into account the specified parameters for the actual Green's function. A set of linear differential equation