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

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

\frac{d}{d x} (2 x^{2})

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\int sec (x) \cdot tan^{2} (x) d x

\int_{l n (4)}^{l n (16)} e^{\frac{x}{2}} d x

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