Can You Solve This Calculus Puzzle? | (f′+f″)/(f‴−f″) =2? IITian’s -Substitution Trick! 🔑

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Can You Solve This Calculus Puzzle? | (f′+f″)/(f‴−f″) =2?

Use this IITian’s -Substitution Trick! 🔑in this video made by an IItian for the aspirants of JEE Mains, JEE advanced, CSIR NET mathematics.

Welcome to the channel maths&science by iitian.

🎯 Master ODEs the IIT Way! — A must-watch for JEE Main/Advanced, CSIR-NET, GATE & CMI/ISI aspirants!

In this crisp, insight-packed video by an IITian educator, we solve a high-level differential equation:
➡️ (f′ + f″) / (f‴ − f″) = 2

and transform it—from a nonlinear-looking expression—into a solvable linear ODE using smart reduction techniques.

✨ What You’ll Gain:
✔️ Step-by-step strategy to reduce order and simplify complex derivative ratios
✔️ How to avoid pitfalls (e.g., singular cases where denominator = 0)
✔️ Solving 2nd-order linear ODEs with constant coefficients — even with irrational roots!
✔️ Full derivation of the general solution:
➡️ f(x) = A · e^ [(3 + √17)/4 · x] + B · e^ [(3 − √17)/4 · x] + C
✔️ Conceptual clarity + exam-smart execution — exactly what JEE & CSIR-NET demand!

📌 Ideal for:
• JEE Main & Advanced (Calculus, Functions)
• CSIR-NET / GATE Mathematics (ODEs, Real Analysis prep)
• CMI / ISI / Olympiad aspirants seeking elegant problem-solving
• Teachers & content creators looking for clean, rigorous explanations

💡 This problem tests logical reduction, not just formula recall — a hallmark of top-tier exams. Learn how to see structure in chaos, the IIT way.

🔔 Subscribe for more deep-dive, exam-critical math content — where clarity meets competitiveness!

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MATHEMATICS BY IITIAN

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Channel Name: MATHS&SCIENCE BY IITIAN
Handle: @mathsciencebyiitian
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