Runge–Kutta Method of Order 4 | Solve dy/dx = (y² − x²)/(y² + x²) | VTU Numerical Methods

🔥 Learn Runge-Kutta Method (RK4) with another important VTU Numerical Methods problem solved step-by-step. Perfect for VTU exam preparation, assignments, concept clarity, and last-minute revision. ━━━━━━━━━━━━━━━━━━━━━ 📘 Subject Mapping: 📚 Numerical Solution of Differential Equations for: • 1BMATS201 – Module 5 • 1BMATE201 – Module 4 • 1BMATC201 – Module 4 • 1BMATM201 – Module 4 ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question: Find an approximate solution of dy/dx = (y² − x²)/(y² + x²), y(0) = 1 at x = 0.2 using Runge-Kutta Method of fourth order. ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: ✔ Runge-Kutta Method of Fourth Order (RK4) ✔ Numerical Solution of Differential Equations ✔ Nonlinear Differential Equations ✔ Calculation of k₁, k₂, k₃ and k₄ ✔ Step-by-step VTU Problem Solving ✔ Important Repeated VTU Questions ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ RK4 Method Problem 5    • Don't Miss This RK4 Problem! | (x + y)dy/d...   2️⃣ RK4 Method Problem 6    • RK4 Method Calculation | Important Problem...   3️⃣ Modified Euler’s Method    • Modified Euler’s Method | Solve dy/dx = 3x...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish) 🔥 Numerical Solution of Differential Equations Playlist 👉    • VTU Numerical Solution of Differential Equ...   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Method 📌 Modified Euler’s Method    • Modified Euler’s Method | Solve dy/dx = x²...   📌 Milne’s Predictor Corrector Method    • Don't Miss This! Milne’s Predictor-Correct...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Continue with more RK4 Method problems and master nonlinear differential equation solving techniques for VTU exams. ━━━━━━━━━━━━━━━━━━━━━ 📙 All 1BMATS201 Playlists: 📌 M1 (Imp) VTU Numerical Methods Problems Solved | Bisection, Regula Falsi & Newton–Raphson 👉    • 1BMATS201 Module 1 | Numerical Methods | B...   📌 M1 👉    • 1BMATS201 Module-1: Introduction to Numeri...   📌 M2 (Imp) 1BMATS201 Module-2: Numerical solutions for system of linear equations | VTU 👉    • 1BMATS201 Module-2: Numerical solutions fo...   📌 M3 (Imp) Interpolation Methods in Numerical Methods | Newton Forward, Divided Difference & Lagrange 👉    • Interpolation Methods in Numerical Methods...   📌 M3 👉    • 1BMATS201 Module-3: Interpolation   📌 M4 (Bernoulli’s) 1BMATS201 Bernoulli Differential Equations 🔥 | All Important Problems | VTU Module 4 👉    • 1BMATS201 Bernoulli Differential Equations...   📌 M4 👉    • 1BMATS201 Module-4: Differential Equations...   📌 M5 (Imp) VTU Numerical Solution of Differential Equations | Taylor Series, RK4, Modified Euler & Milne Method 👉    • VTU Numerical Solution of Differential Equ...   📌 M5 👉    • 1BMATS201 Module-5: Numerical Integration ...   ━━━━━━━━━━━━━━━━━━━━━ 📙 All 1BMATE201 Playlists: 📌 M1 👉    • 1BMATE201 Module 1 | Double Integrals, Tri...   📌 M2 👉    • Vector Calculus & Applications | VTU 1BMAT...   📌 M3 (Imp) Numerical Methods 1 VTU Playlist | Regula Falsi, Newton Raphson, Interpolation & Numerical Integration 👉    • Numerical Methods 1 VTU Playlist | Regula ...   📌 M3 👉    • 1BMATE201 Module 3 | Numerical Methods I |...   📌 M4 (Imp) VTU Numerical Solution of Differential Equations | Taylor Series, RK4, Modified Euler & Milne Method 👉    • VTU Numerical Solution of Differential Equ...   📌 M4 👉    • 1BMATE201 Module 4 | Numerical Methods II ...   📌 M5 👉    • 1BMATE201 Module-5: Laplace transforms   ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ #RungeKuttaMethod #RK4Method #NumericalMethods #DifferentialEquations #VTUMaths #1BMATS201 #EngineeringMathematics