What is the solution for (dy)/(dx)=5+sqrt(y-5x+2) ?

The solution for (dy)/(dx)=5+sqrt(y-5x+2) is y=(x^2+c_{1}^2)/4+(c_{1}x)/2+5x-2

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(dy)/(dx)=5+sqrt(y-5x+2)

\frac{d y}{d x} = 5 + y - 5 x + 2

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 5 x - 2

Solution steps

\frac{d y}{d x} = 5 + y - 5 x + 2

Solve using substitution:

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 5 x - 2

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 5 x - 2

x^{2} y^{^{'}} + \frac{4}{3} x y = 2 cos (3 x) y^{- \frac{1}{2}}

\frac{\partial}{\partial x} (3 x^{2} \cdot c)

t^{2} y^{^{'}} + t y = 3

\int \frac{x}{x ^{2}} d x

x^{2} y^{^{'}} + x y = 3 y^{3}

What is the solution for (dy)/(dx)=5+sqrt(y-5x+2) ?
The solution for (dy)/(dx)=5+sqrt(y-5x+2) is y=(x^2+c_{1}^2)/4+(c_{1}x)/2+5x-2