What is the solution for derivative of 3f(x+2x)x=5 ?

The solution for derivative of 3f(x+2x)x=5 is f(x)= 5/3+(c_{1}}{3x}-\frac{2x)/3

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derivative of 3f(x+2x)x=5

\frac{d}{d x} (3 f (x) + 2 x) x = 5

f (x) = \frac{5}{3} + \frac{c _{1}}{3 x} - \frac{2 x}{3}

Solution steps

\frac{d}{d x} ((3 f (x) + 2 x) x) = 5

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

(3 f (x) + 2 x) x = \int 5 d x

\int 5 d x = 5 x + c_{1}

(3 f (x) + 2 x) x = 5 x + c_{1}

Isolate

f (x) : f (x) = \frac{5}{3} + \frac{c _{1}}{3 x} - \frac{2 x}{3}

f (x) = \frac{5}{3} + \frac{c _{1}}{3 x} - \frac{2 x}{3}

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What is the solution for derivative of 3f(x+2x)x=5 ?
The solution for derivative of 3f(x+2x)x=5 is f(x)= 5/3+(c_{1}}{3x}-\frac{2x)/3