 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/3/a/solution

e^{y}

e^{y} y^{'} = e^{x}

. The left side is

(e^{y})^{'}

, hence

e^{y} = e^{x} + C

. Therefore

y (x) = ln (e^{x} + C), e^{x} + C > 0.

The real general solution is taken on any connected interval where the logarithm's argument is positive.

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