Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.
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Differential Equations

Previous Year Questions (2022-2024)

📅 Year 2022

  1. Solve: dydx + y = e^{-x}.
    Show Solution
    Linear DE. IF = e^{∫dx} = ex\nyex = ∫ex e^{-x}dx = ∫dx = x + C\ny = (x+C)e^{-x}
  2. Form DE for y = A cos 2x + B sin 2x.
    Show Solution
    y = A cos 2x + B sin 2x\ndy/dx = -2A sin 2x + 2B cos 2x\nd2y/dx2 = -4A cos 2x - 4B sin 2x = -4y\nDE: d2y/dx2 + 4y = 0

📅 Year 2023

  1. Solve: dydx + y = e^{-x}.
    Show Solution
    Linear DE. IF = e^{∫dx} = ex\nyex = ∫ex e^{-x}dx = ∫dx = x + C\ny = (x+C)e^{-x}
  2. Form DE for y = A cos 2x + B sin 2x.
    Show Solution
    y = A cos 2x + B sin 2x\ndy/dx = -2A sin 2x + 2B cos 2x\nd2y/dx2 = -4A cos 2x - 4B sin 2x = -4y\nDE: d2y/dx2 + 4y = 0

📅 Year 2024

  1. Solve: dydx + y = e^{-x}.
    Show Solution
    Linear DE. IF = e^{∫dx} = ex\nyex = ∫ex e^{-x}dx = ∫dx = x + C\ny = (x+C)e^{-x}
  2. Form DE for y = A cos 2x + B sin 2x.
    Show Solution
    y = A cos 2x + B sin 2x\ndy/dx = -2A sin 2x + 2B cos 2x\nd2y/dx2 = -4A cos 2x - 4B sin 2x = -4y\nDE: d2y/dx2 + 4y = 0