What is the solution for derivative of tan(y)=x ?

The solution for derivative of tan(y)=x is y=arctan((x^2)/2+c_{1})+pin

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derivative of tan(y)=x

\frac{d}{d x} (tan (y)) = x

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

Solution steps

\frac{d}{d x} (tan (y)) = x

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

then

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

tan (y) = \int x d x

\int x d x = \frac{x ^{2}}{2} + c_{1}

tan (y) = \frac{x ^{2}}{2} + c_{1}

Isolate

y : y = arctan (\frac{x ^{2}}{2} + c_{1}) + πn

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

(x y^{2} + 3 y^{2}) d y - 9 y d x = 0

\frac{d y}{d x} = \frac{2 x}{y}, y (1) = 1

x d y = (\frac{1}{y ^{2}} - y) d x

\frac{d y}{d x} = \frac{3 x ^{2} - e ^{x}}{2 y - 5}, y (0) = 1

y^{^{'}} = y^{2} \cdot x

What is the solution for derivative of tan(y)=x ?
The solution for derivative of tan(y)=x is y=arctan((x^2)/2+c_{1})+pin