CF - PI|Higher Order Differential Equation Constant Coefficient|Engineering Math Sem2|BTech|BCA|BSc скачать в хорошем качестве

CF - PI|Higher Order Differential Equation Constant Coefficient|Engineering Math Sem2|BTech|BCA|BSc

WATSUP LINK : - https://chat.whatsapp.com/CBT7Fk4LqPW... APP LINK :-https://play.google.com/store/apps/de.... App name:- dhi learn and grow for notes Engineering math sem -2 : https://www.onlinetutorialbyvaishali.... In this lecture, we study Higher Order Linear Differential Equations with Constant Coefficients including complete theory of Complementary Function (CF) and Particular Integral (PI). This topic is very important for:-B.Tech | BCA | B.Sc | M.Sc | BBA Engineering Mathematics Semester 2 University Exams Competitive Exams In this video, you will learn: • Definition of Higher Order Differential Equation • Linear Differential Equation with Constant Coefficients • Method to find Complementary Function (CF) • Auxiliary Equation concept • Different cases of roots (Real, Repeated, Complex) • Methods to find Particular Integral (PI) • Shortcut tricks for fast solving in exams 📘 THEORY: Higher Order Differential Equation with Constant Coefficient 1️⃣ Definition A differential equation involving derivatives of order greater than one is called a Higher Order Differential Equation. General form: aₙ Dⁿy + aₙ₋₁ Dⁿ⁻¹y + ... + a₁ Dy + a₀ y = X(x) Where: D = d/dx a₀, a₁, ..., aₙ are constants If RHS = 0 → Homogeneous If RHS ≠ 0 → Non-homogeneous 2️⃣ Solution Structure Complete Solution = Complementary Function (CF) + Particular Integral (PI) y = CF + PI 🔵 Complementary Function (CF) Solve the homogeneous equation: aₙ Dⁿy + ... + a₀ y = 0 Step 1: Form Auxiliary Equation (AE) Replace: D² → m² D → m Solve: aₙ mⁿ + aₙ₋₁ mⁿ⁻¹ + ... + a₀ = 0 Case 1: Distinct Real Roots If roots = m₁, m₂. CF = C₁ e^(m₁x) + C₂ e^(m₂x) Case 2: Repeated Roots If root m repeated twice: CF = (C₁ + C₂ x)e^(mx) Case 3: Complex Roots If roots = α ± iβ : CF = e^(αx) [C₁ cos(βx) + C₂ sin(βx)] This lecture is explained in simple classroom style for university students. If you are preparing for Engineering Maths Sem-2, this topic is compulsory for scoring high marks. Subscribe to Online Tutorial by Vaishali for complete Engineering Maths series. #EngineeringMaths #HigherOrderDE #CFandPI #DifferentialEquations #BTechMaths #ODE #Sem2Maths #MathsByVaishali #EngineeringStudents #UniversityExams