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Solve the differential equation dy/dx = 1 + x + y + xy with the initial condition y(-1) = 0. The solution y(x) is
- e^((1-x)²/2)
- e^((1+x)²/2) - 1
- logₑ(1 + x) - 1
- 1 + x
Correct answer: e^((1+x)²/2) - 1
Solution
Separating gives ln(1+y) = (1+x)²/2 + C; applying y(-1)=0 fixes C = 0.
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