What is the solution for (dy)/(dx)+5(tan(5x))y=4cos(5x) ?

The solution for (dy)/(dx)+5(tan(5x))y=4cos(5x) is y=(4x)/(sec(5x))+(c_{1})/(sec(5x))

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(dy)/(dx)+5(tan(5x))y=4cos(5x)

\frac{d y}{d x} + 5 (tan (5 x)) y = 4 cos (5 x)

y = \frac{4 x}{sec ( 5 x )} + \frac{c _{1}}{sec ( 5 x )}

Solution steps

\frac{d y}{d x} + 5 (tan (5 x)) y = 4 cos (5 x)

Solve linear ODE:

y = \frac{4 x}{sec ( 5 x )} + \frac{c _{1}}{sec ( 5 x )}

y = \frac{4 x}{sec ( 5 x )} + \frac{c _{1}}{sec ( 5 x )}

x \to 0 + lim (\frac{x ^{2}}{4} - \frac{2}{x})

\frac{d}{d x} (x (x + 4))

\int sec^{2} (5 x t a) n^{3} 5 x d x

\int cos (x) cos (5 x) d x

f (x) = x^{2}, (1, 5), 5

What is the solution for (dy)/(dx)+5(tan(5x))y=4cos(5x) ?
The solution for (dy)/(dx)+5(tan(5x))y=4cos(5x) is y=(4x)/(sec(5x))+(c_{1})/(sec(5x))