Ulam Stability for Third-Order Linear Differential Equations with Variable Coefficients

This study explores the Ulam stability of third-order differential equation h(t)x”'+e(t)x”+f(t)x'+g(t)x=0 with a new approach, where e , f , g and h are real-valued variable coefficients. The claim of the main result is that if two differential equations different from the above equation have a complex-valued solution on an interval I , then Ulam stability for the above equation is guaranteed on I . In addition, an explicit Ulam constant is also derived. The results are applied to Euler differential equations and constant coefficients differential equations.