Differential Equations Class 12 Maths Notes – Formulas & Quick Revision

Differential Equations mein order-degree, variable separable, homogeneous aur linear DE solve karna aata hai. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Differential Equations

• Order = highest derivative; degree = uski power (polynomial form mein)
• Variable separable: f(y)dy = g(x)dx → integrate both
• Homogeneous: y = vx substitute karo
• Linear DE: dy/dx + Py = Q
• Integrating factor: IF = e^∫Pdx
• Solution: y·IF = ∫(Q·IF)dx + C
• General solution mein arbitrary constants = order
• Particular solution: initial condition se C nikalo

Quick Revision Points

• Linear DE ka 6-marker boards mein regular hai
• IF nikalte waqt ∫P dx mein constant mat lagao
• Homogeneous pehchano: har term ki degree same
• dx/dy + Px = Q form bhi ho sakti hai (x ko dependent lo)
• Curves ke through DE banana bhi syllabus mein hai

FAQ

Linear DE ka format kya hai?

Standard form mein lao → IF → y·IF = ∫Q·IF — PDF mein 3-step solved pattern hai.

Kaunsa method kab lagau?

PDF ka identification flowchart: separable → homogeneous → linear, isi order mein check karo.

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