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)

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✅ YouTube Tags

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