What is the solution for (dy)/(dx)=5+sqrt(y-5x+8) ?

The solution for (dy)/(dx)=5+sqrt(y-5x+8) is y=(x^2+c_{1}^2)/4+(c_{1}x)/2+5x-8

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(dy)/(dx)=5+sqrt(y-5x+8)

\frac{d y}{d x} = 5 + y - 5 x + 8

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 5 x - 8

Solution steps

\frac{d y}{d x} = 5 + y - 5 x + 8

Solve using substitution:

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 5 x - 8

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} + 5 x - 8

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\frac{d y}{d t} = ln (5 t - 4)

What is the solution for (dy)/(dx)=5+sqrt(y-5x+8) ?
The solution for (dy)/(dx)=5+sqrt(y-5x+8) is y=(x^2+c_{1}^2)/4+(c_{1}x)/2+5x-8