What is the solution for f^'(x)=(2x)/((2x-1))f(x) ?

The solution for f^'(x)=(2x)/((2x-1))f(x) is f(x)=e^{x-1/2+c_{1}}sqrt(2x-1)

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f^'(x)=(2x)/((2x-1))f(x)

f^{^{'}} (x) = \frac{2 x}{( 2 x - 1 )} f (x)

f (x) = e^{x - \frac{1}{2} + c_{1}} 2 x - 1

Solution steps

f^{'} (x) = \frac{2 x}{( 2 x - 1 )} f (x)

Solve separable ODE:

f (x) = e^{x - \frac{1}{2} + c_{1}} 2 x - 1

f (x) = e^{x - \frac{1}{2} + c_{1}} 2 x - 1

\frac{d y}{d x} = y x^{2} - 1.2 y

y = y^{^{'}} \cdot (t^{2} - 14 t + 40)

\frac{d y}{d x} = \frac{x ^{2}}{y}, y = 2

\frac{y ^{^{'}}}{x} = e^{y + x^{2}}

\frac{d y}{d x} + \frac{x y}{x ^{2} - 9} = 0

What is the solution for f^'(x)=(2x)/((2x-1))f(x) ?
The solution for f^'(x)=(2x)/((2x-1))f(x) is f(x)=e^{x-1/2+c_{1}}sqrt(2x-1)