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Class 12 Differential Equations · Mcq Single Correct1 Marksseparable_differential_equations

Class 12 Maths · Differential Equations · Mcq Single Correct #14

Find the general solution of y′ = e^(x−y) + x²e^(−y).

(A) y = e^(x−y) − x²e^(−y) + C
(B) eʸ − eˣ = x³/3 + C
(C) eˣ + eʸ = x³/3 + C
(D) eˣ − eʸ = x³/3 + C

✅ Step-by-Step Solution

Final Answer: Option (B): eʸ − eˣ = x³/3 + C

Multiply by eʸ: (eʸ)′ = eˣ + x². Integrate, restricting to eˣ + x³/3 + C > 0.

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