EXERCISE 4.1 | DIFFERENTIAL EQUATIONS | Class 12 Math | FBISE | NBF

EXERCISE 4.1 | DIFFERENTIAL EQUATIONS | Class 12 Math | Federal Board | National Book Foundation In this lecture, we solve Exercise 4.1 (Differential Equations) from Class 12 Mathematics – National Book Foundation (NBF), Federal Board (FBISE). This chapter introduces the basic concepts of differential equations, including order, degree, eliminating arbitrary constants, and verifying solutions. Each question is explained with clear steps to help students prepare for board exams. ▶ TIMESTAMPS 00:00:00 – Q1(i–vii) Find order and degree of differential equations 00:05:50 – Q2(i) Eliminate arbitrary constants 00:10:50 – Q2(ii) Eliminate arbitrary constants 00:13:24 – Q2(iii) Eliminate arbitrary constants 00:15:05 – Q2(iv) Eliminate arbitrary constants 00:17:20 – Q3(i) Verify function as solution of differential equation 00:20:07 – Q3(ii) Verify function as solution 00:24:35 – Q3(iii) Verify function as solution 00:27:55 – Q3(iv) Verify function as solution 00:33:00 – Q3(v) Verify function as solution 00:35:02 – Q3(vi) Verify function as solution 00:37:39 – Q4 Find order & degree of dy/dx · sin x = 0 00:39:16 – Q5 Verify y = a cos x + b sin x is solution of d²y/dx² + y = 0 00:42:15 – Q6(i–ii) Check y₁ = x² and y₂ = x³ as solutions; check linear combination 📚 What This Lecture Covers Meaning of order & degree of differential equations How to eliminate arbitrary constants Verifying a given function as the solution of a differential equation Linear combination of solutions Preparing for Federal Board exam short and long questions Book-based, step-by-step solutions for Exercise 4.1 📝 Book Reference Class 12 Mathematics – National Book Foundation (NBF) Chapter: Differential Equations Exercise: 4.1 🎯 Who Should Watch FSC Part-II students (Pre-Engineering & ICS) Federal Board (FBISE) & Punjab, KPK, Sindh, Balochistan Boards Students preparing for board exams ✅ Hashtags (15) #Class12Math #DifferentialEquations #FBISE #NBF #Exercise41 #FSCPart2 #MathLecture #BoardExamPrep #OrderAndDegree #EliminatingConstants #VerifySolution #MathTutorial #PakistanEducation #IntermediateMath #LearnDifferentialEquations ✅ YouTube Tags Class 12 Math,Differential Equations,Exercise 4.1,NBF Math,FBISE Math,FSC Part 2,Differential equations order degree,Eliminate arbitrary constants,Verify solution differential equation,Class 12 calculus,Math board prep,National Book Foundation Math,Math lecture Pakistan,DE solutions class 12,Intermediate mathematics,FBISE chapter 4