Verification of Particular Solution yₚ Using Leibniz Integral Rule | Variation of Parameters | ODEs

*Verification of the Particular Solution \(y_p\) Using Leibniz Integral Rule | Variation of Parameters | Mathematical Methods for Physicists* Welcome to **ZetaMathPhys**! In this lecture, we verify the particular solution \(y_p\) obtained using the *method of variation of parameters* by applying the **Leibniz integral rule**. We differentiate the integral expressions carefully, evaluate the required derivatives, and substitute the results into the original nonhomogeneous second-order linear ordinary differential equation to verify that the particular solution satisfies the equation. 📚 *Topics covered:* Variation of parameters for nonhomogeneous ODEs Particular solution \(y_p\) Leibniz integral differentiation rule First and second derivatives of integral expressions Substitution into the original differential equation Step-by-step verification of the particular solution This lecture is useful for BS Physics, MS Physics, and students studying mathematical physics, applied mathematics, and differential equations. 📖 *Reference:* Mathematical Methods for Physicists by Arfken, Weber & Harris Subscribe to *ZetaMathPhys* for more tutorials on differential equations, mathematical methods, and applied mathematics. ✅ Educational videos uploaded regularly. 🔔 Subscribe and click the bell icon to stay updated. verification of particular solution, verify yp using Leibniz rule, Leibniz integral rule, Leibniz rule for differentiation under integral sign, variation of parameters, particular solution of ODE, verification of yp, nonhomogeneous second order ODE, second order linear differential equations, differentiation under integral sign, Leibniz rule examples, Green's function, mathematical methods for physicists, Arfken Weber Harris, differential equations for physicists, mathematical physics, applied mathematics, BS Physics, MS Physics, ZetaMathPhys #LeibnizRule #LeibnizIntegralRule #VariationOfParameters #ParticularSolution #NonhomogeneousODE #DifferentialEquations #MathematicalMethodsForPhysicists #Arfken #MathematicalPhysics #AppliedMathematics #BSPhysics #MSPhysics #ZetaMathPhys