Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Concept 🎬 Exact DE Trick JEE mein jab differential equation dikhe: M ( x , y )   d y + N ( x , y )   d x = 0 sabse pehla sawaal hona chahiye 👇 👉 “Kya yeh exact hai?” Agar exact nikla — solution almost direct mil jaata hai . 🖼️ Concept Image ✍️ Short Explanation Exact DE questions JEE ke sabse scoring problems hote hain. Reason simple hai: 👉 Na substitution 👉 Na heavy algebra 👉 Sirf partial derivatives + integration 🔹 Step 1 — Form of an Exact Differential Equation Given form: M ( x , y )   d y + N ( x , y )   d x = 0 M(x,y)\,dy + N(x,y)\,dx = 0 ✅ Exactness Condition: ∂ M ∂ x = ∂ N ∂ y 📌 Agar dono equal aa jaayein: DE exact hai Direct integration allowed Agar equal nahi: Phir integrating factor ka case hota hai (alag topic) 🔹 Step 2 — Meaning of Exactness Exact hone ka matlab 👇 Ek function F ( x , y ) F(x,y)  exist karta hai aisa ki: d F = M   d y + N   d x dF = M\,dy + N\,dx Isliye DE ka general solution hota hai: F ( x...