What is the solution for (dy)/(dx)=4+sqrt(y-4x+6) ?

The solution for (dy)/(dx)=4+sqrt(y-4x+6) is y=(x^2+c_{1}^2)/4+(c_{1}x)/2+4x-6

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(dy)/(dx)=4+sqrt(y-4x+6)

\frac{d y}{d x} = 4 + y - 4 x + 6

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 4 x - 6

Solution steps

\frac{d y}{d x} = 4 + y - 4 x + 6

Solve using substitution:

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 4 x - 6

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 4 x - 6

What is the solution for (dy)/(dx)=4+sqrt(y-4x+6) ?
The solution for (dy)/(dx)=4+sqrt(y-4x+6) is y=(x^2+c_{1}^2)/4+(c_{1}x)/2+4x-6