Differential Equations

Let the tangent at any point P on a curve passing through the points (1, 1) and \(\left(\frac{1}{10}, 100\right)\), intersect positive \(x\)-axis and \(y\)-axis at the points A and B respectively. If \(\mathrm{PA}: \mathrm{PB}=1: k\) and \(y=y(x)\) is the solution of the differential equation \(e^{\frac{d y}{d x}}=k x+\frac{k}{2}, y(0)=k\), then \(4 y(1)-6 \log _{\mathrm{e}} 3\) is equal to ____________.