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)

(D^{2} - 1) y = e^{x}

y^{^{''}} + \frac{53}{7} \cdot y^{^{'}} + 49 x = 0

2 y^{^{''}} - 18 y^{^{'}} = 6 tan (3 x)

D (f (x)) = 4 sec (4 x) tan (4) (x)

2 y^{^{''}} + 9 y^{^{'}} + 9 y = 2 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)