What is the solution for (x-yarctan(y/x))dx+xarctan(y/x)dy=0 ?

The solution for (x-yarctan(y/x))dx+xarctan(y/x)dy=0 is y=-\W(-1/(c_{1)x})x

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(x-yarctan(y/x))dx+xarctan(y/x)dy=0

(x - y arctan (\frac{y}{x})) d x + x arctan (\frac{y}{x}) d y = 0

y = - W (- \frac{1}{c _{1} x}) x

Solution steps

(x - y arctan (\frac{y}{x})) d x + x arctan (\frac{y}{x}) d y = 0

Solve using substitution:

y = - W (- \frac{1}{c _{1} x}) x

y = - W (- \frac{1}{c _{1} x}) x

h (x) = \frac{2}{x ^{5}} + \frac{1}{x ^{7}}

\int_{- 1}^{1} x (x^{2} + 1)^{3} d x

x^{2} y^{^{''}} + x y^{^{'}} - 4 y = x^{2} + x

\frac{d ^{3}}{d x ^{3}} (x^{4} - 6 x^{3})

14 t^{2}

What is the solution for (x-yarctan(y/x))dx+xarctan(y/x)dy=0 ?
The solution for (x-yarctan(y/x))dx+xarctan(y/x)dy=0 is y=-\W(-1/(c_{1)x})x