What is the solution for y^{''}+y=-sec(x) ?

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

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y^{''}+y=-sec(x)

y^{^{''}} + y = - sec (x)

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

Solution steps

y^{''} (x) + y = - sec (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)

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