What is a solution to the differential equation $dy/dx=2y-1$ ?

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Answer 1 · 2016-08-23T09:39:14

$y = (C_2 e^{2x}+1)/2$

Substituting $z = 2y-1$ in $dy/dx=2y-1$

and considering

$dz/(dx) = 2 dy/(dx)$ we have

$1/2 dz/dx = z$ . Grouping variables

$dz/z = 2 dx$ and integrating

$log_e z = 2 x + C_1$ or equivalently

$z = C_2e^{2x} = 2 y -1$ and finally

$y = (C_2 e^{2x}+1)/2$

What is a solution to the differential equation dy/dx=2y-1dy/dx=2y-1?