What is the solution for (dy)/(dx)+10(tan(10x))y=-cos(10x) ?

The solution for (dy)/(dx)+10(tan(10x))y=-cos(10x) is y=-x/(sec(10x))+(c_{1})/(sec(10x))

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(dy)/(dx)+10(tan(10x))y=-cos(10x)

\frac{d y}{d x} + 10 (tan (10 x)) y = - cos (10 x)

y = - \frac{x}{sec ( 10 x )} + \frac{c _{1}}{sec ( 10 x )}

Solution steps

\frac{d y}{d x} + 10 (tan (10 x)) y = - cos (10 x)

Solve linear ODE:

y = - \frac{x}{sec ( 10 x )} + \frac{c _{1}}{sec ( 10 x )}

y = - \frac{x}{sec ( 10 x )} + \frac{c _{1}}{sec ( 10 x )}

\int \frac{( x ^{3} )}{x ^{2} + 100} d x

e^{r x}

\frac{d}{d x} (- e^{- x} x^{2} + 6 e^{- x} x - 6 e^{- x})

\int cot^{3} (10 x) d x

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = 1

What is the solution for (dy)/(dx)+10(tan(10x))y=-cos(10x) ?
The solution for (dy)/(dx)+10(tan(10x))y=-cos(10x) is y=-x/(sec(10x))+(c_{1})/(sec(10x))