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

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

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y^{''}+y= 1/(cos(x))

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 8 y^{^{'}} = 8 x

y^{^{''}} - 2 y^{^{'}} = x^{3}

y^{^{''}} + 4 y = 2 sec^{3} (2 t)

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 12

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{3 x}}{1 + e ^{x}}

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