What is the solution for y^{''}+y= 2/(cos(x)) ?

The solution for y^{''}+y= 2/(cos(x)) is y=c_{1}cos(x)+c_{2}sin(x)+2ln(cos(x))cos(x)+2xsin(x)

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y^{''}+y= 2/(cos(x))

y^{^{''}} + y = \frac{2}{cos ( x )}

y = c_{1} cos (x) + c_{2} sin (x) + 2 ln (cos (x)) cos (x) + 2 x sin (x)

Solution steps

y^{''} (x) + y = \frac{2}{cos ( x )}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 2 ln (cos (x)) cos (x) + 2 x sin (x)

y = c_{1} cos (x) + c_{2} sin (x) + 2 ln (cos (x)) cos (x) + 2 x sin (x)

y^{^{''}} - 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} t^{- 1}

y^{^{''}} - 4 y^{^{'}} + 13 y = - 40 cos (x) + 13 x

y^{^{''}} + 25 y = cos (5 x) csc^{2} (5 x)

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 e^{- x}

What is the solution for y^{''}+y= 2/(cos(x)) ?
The solution for y^{''}+y= 2/(cos(x)) is y=c_{1}cos(x)+c_{2}sin(x)+2ln(cos(x))cos(x)+2xsin(x)