What is the solution for y^'+tan(x)y= 1/(cos(x)) ?

The solution for y^'+tan(x)y= 1/(cos(x)) is y=(tan(x))/(sec(x))+(c_{1})/(sec(x))

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y^'+tan(x)y= 1/(cos(x))

y^{^{'}} + tan (x) y = \frac{1}{cos ( x )}

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

Solution steps

y^{'} (x) + tan (x) y = \frac{1}{cos ( x )}

Solve linear ODE:

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

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

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What is the solution for y^'+tan(x)y= 1/(cos(x)) ?
The solution for y^'+tan(x)y= 1/(cos(x)) is y=(tan(x))/(sec(x))+(c_{1})/(sec(x))