What is the solution for y^'+ytan(t)=(tan(t))/(cos(t)) ?

The solution for y^'+ytan(t)=(tan(t))/(cos(t)) is y=(tan^2(t))/(2sec(t))+(c_{1})/(sec(t))

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y^'+ytan(t)=(tan(t))/(cos(t))

y^{^{'}} + y tan (t) = \frac{tan ( t )}{cos ( t )}

y = \frac{tan ^{2} ( t )}{2 sec ( t )} + \frac{c _{1}}{sec ( t )}

Solution steps

y^{'} (t) + y tan (t) = \frac{tan ( t )}{cos ( t )}

Solve linear ODE:

y = \frac{tan ^{2} ( t )}{2 sec ( t )} + \frac{c _{1}}{sec ( t )}

y = \frac{tan ^{2} ( t )}{2 sec ( t )} + \frac{c _{1}}{sec ( t )}

What is the solution for y^'+ytan(t)=(tan(t))/(cos(t)) ?
The solution for y^'+ytan(t)=(tan(t))/(cos(t)) is y=(tan^2(t))/(2sec(t))+(c_{1})/(sec(t))