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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

y = \frac{1}{x + 1}, y = x + 2, x = 2

\frac{d}{d x} ((x + 1)^{x})

\int \frac{( y ^{4} + 2 y ^{2} - 1 )}{y} d y

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