What is the solution for (x^2+81)((dy)/(dx))=2,y(9)=0 ?

The solution for (x^2+81)((dy)/(dx))=2,y(9)=0 is y= 2/9 arctan(x/9)-pi/(18)

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(x^2+81)((dy)/(dx))=2,y(9)=0

(x^{2} + 81) (\frac{d y}{d x}) = 2, y (9) = 0

y = \frac{2}{9} arctan (\frac{x}{9}) - \frac{π}{18}

Solution steps

(x^{2} + 81) (\frac{d y}{d x}) = 2

Substitute

\frac{d y}{d x}

with

y^{'} (x)

(x^{2} + 81) (y^{^{'}} (x)) = 2

Isolate

y^{'} (x) : y^{'} (x) = \frac{2}{x ^{2} + 81}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{2}{x ^{2} + 81} d x

\int \frac{2}{x ^{2} + 81} d x = \frac{2}{9} arctan (\frac{x}{9}) + c_{1}

y = \frac{2}{9} arctan (\frac{x}{9}) + c_{1}

Apply initial conditions:

y = \frac{2}{9} arctan (\frac{x}{9}) - \frac{π}{18}

y = \frac{2}{9} arctan (\frac{x}{9}) - \frac{π}{18}

(x + 2)^{2} + (y - 3)^{2} = 37, (4, 2)

y^{^{'}} = r - k y

x \to - 1 lim (x ∣ x + 1 ∣)

f (x) = 7 y^{7} - 4 y^{6} + 35 y^{4} - 24 y^{2}

x \to 0 lim (\frac{( ( x ^{2} + 3 ) )}{x})

What is the solution for (x^2+81)((dy)/(dx))=2,y(9)=0 ?
The solution for (x^2+81)((dy)/(dx))=2,y(9)=0 is y= 2/9 arctan(x/9)-pi/(18)