Question
45 of
100
Question Palette
The solution of the differential equation dy/dx = e^(x − y) + x²e^(−y) is:
A
y = e^(x−y) − x²e^(−y) + c
Correct Option:
B
Explanation
Given dy/dx = e^(x − y) + x²e^(−y), multiply throughout by eʸ: eʸ(dy/dx) = eˣ + x². Since eʸ(dy/dx) = d(eʸ)/dx, integrating gives eʸ = eˣ + x³/3 + C. Hence eʸ − eˣ = x³/3 + C.
