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Let y = y(x) solve the differential equation ((5 + e^x)/(2 + y))*dy/dx + e^x = 0 with y(0) = 1. Find the value of |y(logₑ 13)|.
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Correct answer: 1
Solution
Separating and integrating gives (2+y)(5+e^x) = 18 from the initial condition; at x = ln13 this yields y = -1, so |y| = 1.
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