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

The solution for (dy)/(dx)=sqrt((3y-2)/(2x+1)) is y=(3(x+c_{1}sqrt(2x+1)))/2+(3(c_{1}^2+1))/4+2/3

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

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

y = \frac{3 ( x + c _{1} 2 x + 1 )}{2} + \frac{3 ( c _{1}^{2} + 1 )}{4} + \frac{2}{3}

Solution steps

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

Solve separable ODE:

y = \frac{3 ( x + c _{1} 2 x + 1 )}{2} + \frac{3 ( c _{1}^{2} + 1 )}{4} + \frac{2}{3}

y = \frac{3 ( x + c _{1} 2 x + 1 )}{2} + \frac{3 ( c _{1}^{2} + 1 )}{4} + \frac{2}{3}

x \to 2 lim (\frac{e ^{3}}{x})

(ln (\frac{1}{x}))^{^{'}}

6 x

\frac{d}{d p} (\frac{( 10 p ^{0.25} + 1 )}{p ^{0.25}})

\int_{2}^{4} x^{2} \frac{( 2 x - 3 )}{6} d x

What is the solution for (dy)/(dx)=sqrt((3y-2)/(2x+1)) ?
The solution for (dy)/(dx)=sqrt((3y-2)/(2x+1)) is y=(3(x+c_{1}sqrt(2x+1)))/2+(3(c_{1}^2+1))/4+2/3