Let y=y(x) be the solution of the differential equation {dy}={e}^{\\alphax+y} {dx} ; \\alpha \\in{N} . If {y}(\log _{{e}} 2)=\log _{{e}} 2and y(0)=\log _{e}(\frac{1}{2}), then the value of \\alpha is equal to ____. [27 Jul 2021 Shift 2]

Differential Equations Part 1

Section: Mathematics

Question : 9 of 100

Marks: +1, -0

Let y=y(x) be the solution of the differential equation dy=eαx+ydx;α∈N. If y(loge2)=loge2and y(0)=loge(

), then the value of α is equal to ____.

[27 Jul 2021 Shift 2]

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