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Find the general solution of the differential equation (x + y + 1) dy = dx.

1. x + y + 2 = C e^y
2. x + y + 4 = C log y
3. log(x + y + 2) = C y
4. log(x + y + 2) = C + y

Correct answer: x + y + 2 = C e^y

Solution

Treating x as the function of y gives dx/dy - x = y + 1, whose solution rearranges to x + y + 2 = C e^y.

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