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

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

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y^{''}+y=-sec^2(x)

y^{^{''}} + y = - sec^{2} (x)

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

Solution steps

y^{''} (x) + y = - sec^{2} (x)

Solve linear ODE:

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

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

y^{^{''}} + y = x^{2} + 2

D^{2} (D + 3)^{2} y = 9 e^{- 3 x}

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{6 t}

2 y^{^{''}} + 3 y^{^{'}} + y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{^{'}} = 10 sin (2 x)

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