What is the solution for (cos(x)+ysin(x))dx+(cos(x))dy=0 ?

The solution for (cos(x)+ysin(x))dx+(cos(x))dy=0 is y=-(ln(tan(x)+sec(x)))/(sec(x))+(c_{1})/(sec(x))

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(cos(x)+ysin(x))dx+(cos(x))dy=0

(cos (x) + y sin (x)) d x + (cos (x)) d y = 0

y = - \frac{ln ( tan ( x ) + sec ( x ) )}{sec ( x )} + \frac{c _{1}}{sec ( x )}

Solution steps

(cos (x) + y sin (x)) d x + (cos (x)) d y = 0

Solve linear ODE:

y = - \frac{ln ( tan ( x ) + sec ( x ) )}{sec ( x )} + \frac{c _{1}}{sec ( x )}

y = - \frac{ln ( tan ( x ) + sec ( x ) )}{sec ( x )} + \frac{c _{1}}{sec ( x )}

\frac{\partial}{\partial x} (6 x y e^{- x^{2} - y^{2}})

y = 6 sec (x), at x = \frac{π}{6}

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x^{2} y^{^{''}} + 3 x y^{^{'}} + 3 y = 0

\frac{\partial}{\partial t} (4 t)

What is the solution for (cos(x)+ysin(x))dx+(cos(x))dy=0 ?
The solution for (cos(x)+ysin(x))dx+(cos(x))dy=0 is y=-(ln(tan(x)+sec(x)))/(sec(x))+(c_{1})/(sec(x))