What is the solution for ytan(x)dx+cos^2(x)dy=0 ?

The solution for ytan(x)dx+cos^2(x)dy=0 is y=e^{-(tan^2(x))/2+c_{1}}

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ytan(x)dx+cos^2(x)dy=0

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

y = e^{- \frac{t a n ^{2} ( x )}{2} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{- \frac{t a n ^{2} ( x )}{2} + c_{1}}

y = e^{- \frac{t a n ^{2} ( x )}{2} + c_{1}}

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

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

y^{^{'}} = \frac{( x - 2 ) ^{2}}{y}, y (0) = 1

\frac{d y}{d x} = - \frac{4}{4} x^{4} y^{2}

\frac{d y}{d x} - \frac{y}{x} = 0

What is the solution for ytan(x)dx+cos^2(x)dy=0 ?
The solution for ytan(x)dx+cos^2(x)dy=0 is y=e^{-(tan^2(x))/2+c_{1}}