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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

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