What is the solution for (dy)/(dx)y=sqrt((2x+3)/(x+1)) ?

The solution for (dy)/(dx)y=sqrt((2x+3)/(x+1)) is

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(dy)/(dx)y=sqrt((2x+3)/(x+1))

\frac{d y}{d x} y = \frac{2 x + 3}{x + 1}

y = 2 (\frac{2 x + 3}{2 x + 2} (2 x + 2) + ln (2 x + 3 + 2 x + 2)) + c_{1}, y = - 2 (\frac{2 x + 3}{2 x + 2} (2 x + 2) + ln (2 x + 3 + 2 x + 2)) + c_{1}

Solution steps

\frac{d y}{d x} y = \frac{2 x + 3}{x + 1}

Solve separable ODE:

y = 2 (\frac{2 x + 3}{2 x + 2} (2 x + 2) + ln (2 x + 3 + 2 x + 2)) + c_{1}, y = - 2 (\frac{2 x + 3}{2 x + 2} (2 x + 2) + ln (2 x + 3 + 2 x + 2)) + c_{1}

y = 2 (\frac{2 x + 3}{2 x + 2} (2 x + 2) + ln (2 x + 3 + 2 x + 2)) + c_{1}, y = - 2 (\frac{2 x + 3}{2 x + 2} (2 x + 2) + ln (2 x + 3 + 2 x + 2)) + c_{1}

(x + 3 x y^{2}) d x + e^{x^{2}} y d y = 0

\frac{d}{d θ} (r (θ)) r (θ) = 5 - θ^{3} sin (θ)

y^{^{'}} = e^{(2 + 1) x + (1 + 2) y}

0.001 \cdot y^{^{'}} - \frac{y}{0.001} = 0

y^{2} \frac{d y}{d x} + x^{3} = 0

What is the solution for (dy)/(dx)y=sqrt((2x+3)/(x+1)) ?
The solution for (dy)/(dx)y=sqrt((2x+3)/(x+1)) is