If the solution curve y = f(x) of the differential equation: (x^2 - 4)y' - 2xy + 2x(4 - x^2)^2 | PYQ скачать в хорошем качестве

If the solution curve y = f(x) of the differential equation: (x^2 - 4)y' - 2xy + 2x(4 - x^2)^2 | PYQ

The Question: If the solution curve y = f(x) of the differential equation: (x^2 - 4)y' - 2xy + 2x(4 - x^2)^2 = 0, passes through the point (3, 15), then the local maximum value of f is ________. Mathematical Terms for Easy Search: Differential Equation: (x^2 - 4) dy/dx - 2xy + 2x(4 - x^2)^2 = 0 Initial Condition: f(3) = 15 Domain: x greater than 2 Find: Local maximum value of f(x) Step-by-Step Breakdown: Standard Form: We rewrite the equation into the form dy/dx + P(x)y = Q(x). Integrating Factor (I.F.): Calculating e^integral(P(x)dx) to solve the linear DE. General Solution: Solving for y(x) and using the point (3, 15) to find the constant C. Maxima/Minima: Differentiating the resulting function f(x) and setting f'(x) = 0 to find the point of local maximum. Final Answer: Substituting the critical point back into f(x) to get the final integer/decimal value. This question is a high-yield topic for JEE Main and Advanced aspirants. Watch the full video to master the transition from Differential Equations to Maxima-Minima! Make sure to: ✅ Subscribe for more JEE Main 2026 PYQ solutions and paper analysis. ✅ Like this video if it helped you understand the concept better. ✅ Comment your answer or any specific shift questions you want solved! #JEEMain2026 #DifferentialEquations #Calculus #JEEMaths #IITJEE Preparation #23JanShift2 #MathsPYQ #LocalMaxima #ApplicationOfDerivatives #LinearDifferentialEquation #AbhishekSharmaMaths #ViralMaths Tags (Copy & Paste) JEE Main 2026, JEE Main 23 Jan Shift 2, JEE Main 2026 Math Solution, Linear Differential Equation JEE, (x^2 - 4)y' - 2xy + 2x(4 - x^2)^2 = 0, Local maximum value of f, JEE Math PYQ Solution, Calculus for JEE Main, Application of Derivatives JEE, JEE Main January Attempt 2026, Maths Paper Analysis 2026, IIT JEE Mathematics, Integrating Factor Method. JEE Main 2026 - Paper Solution - 21 January Shift 1 JEE Main 2026 Paper Solution - 21st Jan - Shift 1 Join us on January 21st (Shift 1) for an exclusive walkthrough of the latest JEE Main paper. This is your chance to decode complex problems, learn time-saving hacks, and build a rock-solid foundation for JEE 2026. Start your prep ahead of the curve, mark your calendars and let’s aim for that top percentile together! JEE Main 2026 Paper Analysis | 21 January 1st Shift | Physics • Chemistry • Maths #JEEMains2026 #PaperAnalysis #21JanJEE In this video, we provide a complete paper analysis of JEE Mains 2026 – 21 January 1st Shift. We discuss difficulty level, subject-wise analysis (Physics, Chemistry & Mathematics), good attempts, important questions, and expected cutoff. 👉 Watch till the end for honest analysis & exam insights. #JEEMains2026 #PaperAnalysis #21JanJEE #JEE2026 #JEEMainExam #FirstShift #JEE2026 #JEEMain2026 #JEEPaperSolving #shivangmathsacademy JEE Mains 2026 Exam Review | Physics Chemistry Maths Analysis | Tough ya Easy? JEE Mains 2026 exam ka complete paper review is video mein diya gaya hai. Is video mein Physics, Chemistry aur Maths ka subject wise analysis kiya gaya hai application of derivatives integration class 12 apPhysics paper kaisa tha? 🔹 Ch #JEEMains2026Shift1 #JEEMainsDay1Shift1 #JEE2026 jee mains 2026 shift 1 review jee mains 2026 day 1 shift 1 jee mains 2026 first day first shift review jee mains 2026 shift 1 paper analysis jee mains 2026 chemistry shift 1 jee mains 2026 difficulty level jee mains 2026 expected cutoff shift 1 JEE Main 2026 (First Attempt) LIVE Paper Discussion 🔥 | Shift 1 - 21st Jan 2026 ⚡ #JEEMain20 Overal This JEE Main 2026 live session covers session 1 shift 1 paper analysis. Aakash experts discuss JEE Main 2026 question paper, difficulty level, and subject-wise insights. Students appearing for JEE Main 2026 can use this live discussion for quick evaluation. JEE Main 2026 January 21 Shift 1 & Shift 2 Question Paper with Solutions JEE Main 2026 January 21 Shift 1 Question Paper and Solutions (session 1) JEE Main 2026 January 21 Shift 2 Question Paper & Solutions (Session 1) JEE Main 2026 January 21 Shift 1 Physics Question Paper & Solutions Download PDF JEE Main 2026 January 21 Shift 1 Mathematics Question Paper & Solutions Download PDF JEE Main 2026 January 21 Shift 1 Chemistry Question Paper & Solutions JEE Main 2026 January 21 Shift 2 Physics Question Paper & Solutions JEE Main 2026 January 21 Shift 2 Chemistry Question Paper & Solutions JEE Main 2026 January 21 Shift 2 Mathematics Question Paper & Solutions , jee mains 21 jan paper analysis , 21 jan jee main #jee #jeemains #jeepreparation #jee2026 #jeeexamprep #iit #iitaspirant #jeeaspirants #jeeexam #mostimportanttopics #engineeringentranceexam #iitjeepreparation #jeemain2026 #jee2026 #jeemains #jeeadvanced #jeedropper2026 #jeerepeater #jeeaspirants #jeepreparation #jeestrategy #jeemotivation