The general solution of the differential equation dy/dx = e^(x−y) + x² e⁻ʸ is:
The general solution of the differential equation dy/dx = e^(x−y) + x² e⁻ʸ is:
- A. eʸ = eˣ + x³/3 + C
- B. eʸ = eˣ + x² + C
- C. e⁻ʸ = e⁻ˣ + x³/3 + C
- D. eˣ = eʸ + x³/3 + C
Answer: A) eʸ = eˣ + x³/3 + C
Explanation: Rewriting as dy/dx = e⁻ʸ (eˣ + x²). Multiply by eʸ: eʸ dy = (eˣ + x²) dx. Integrating both sides gives eʸ = eˣ + x³/3 + C.
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