Let a curve \(y = f(x)\) pass through the points \((0, 5) \) and \(\left({\log }_{\mathrm{e}}2,k\right).\) If the curve …

Let a curve \(y = f(x)\) pass through the points \((0, 5) \) and \(\left({\log }_{\mathrm{e}}2,k\right).\) If the curve satisfies the differential equation \(2(3+y){e}^{2x}dx-\left(7+{e}^{2x}\right)dy=0\) then \(k\) is equal to

[JEE Main 2025, 23 Jan (Shift 1)]