What is the solution for sec^2(x)tan(y)dx+sec^2(y)tan(x)dy=0 ?

The solution for sec^2(x)tan(y)dx+sec^2(y)tan(x)dy=0 is y=arctan((c_{1})/(tan(x)))+pin

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sec^2(x)tan(y)dx+sec^2(y)tan(x)dy=0

sec^{2} (x) tan (y) d x + sec^{2} (y) tan (x) d y = 0

y = arctan (\frac{c _{1}}{tan ( x )}) + πn

Solution steps

sec^{2} (x) tan (y) d x + sec^{2} (y) tan (x) d y = 0

Solve separable ODE:

y = arctan (\frac{c _{1}}{tan ( x )}) + πn

y = arctan (\frac{c _{1}}{tan ( x )}) + πn

\frac{y}{x} y^{^{'}} + e^{y} = 0

(t^{2} - 22 t + 96) \frac{d y}{d t} = y

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

\frac{d y}{d x} = 2 e^{x - y}, y (1) = ln (2 e + 1)

e^{3 x} y - e^{5 x} y^{3} y^{^{'}} = 0

What is the solution for sec^2(x)tan(y)dx+sec^2(y)tan(x)dy=0 ?
The solution for sec^2(x)tan(y)dx+sec^2(y)tan(x)dy=0 is y=arctan((c_{1})/(tan(x)))+pin