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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

\int \frac{x + 5 x - 4}{15 x + 9} d x

5 y^{^{''}} + y^{^{'}} = - 4 x

\int \frac{5 x ^{4}}{1 + x ^{10}} d x

\int x^{2} - 6 x + 10 d x

y^{^{''}} - 5 y^{^{'}} = (8 t - 7) sin (2 t)

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