What is the solution for (dy)/(dx)=sqrt(10x+y)-10 ?

The solution for (dy)/(dx)=sqrt(10x+y)-10 is y=(x^2+c_{1}^2)/4+(c_{1}x)/2-10x

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(dy)/(dx)=sqrt(10x+y)-10

\frac{d y}{d x} = 10 x + y - 10

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} - 10 x

Solution steps

\frac{d y}{d x} = 10 x + y - 10

Solve using substitution:

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} - 10 x

y = \frac{x ^{2} + c _{1}^{2}}{4} + \frac{c _{1} x}{2} - 10 x

\frac{\partial}{\partial y} (ln (x y^{2}))

\int \frac{1}{1 - u ^{2}} d u

\frac{A}{y ^{9}} + B e^{y}

\int \frac{3}{x ^{2} + 9} d x

\int \frac{t}{1} d t

What is the solution for (dy)/(dx)=sqrt(10x+y)-10 ?
The solution for (dy)/(dx)=sqrt(10x+y)-10 is y=(x^2+c_{1}^2)/4+(c_{1}x)/2-10x