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
📘 Complete Visual Notes + Formula Sheet PDF
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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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