What is the solution for x^{''}+x=tan(t) ?

The solution for x^{''}+x=tan(t) is x=c_{1}cos(t)+c_{2}sin(t)-cos(t)ln(tan(t)+sec(t))

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x^{''}+x=tan(t)

x^{^{''}} + x = tan (t)

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

Solution steps

x^{''} (t) + x = tan (t)

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 4 y = 3 x + 2

y^{^{''}} + 9 y = 8 sin (t), y (0) = 0, y^{^{'}} (0) = 4

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

y^{^{''}} + 3 y^{^{'}} + 2 y = 10 e^{3 t}

y^{^{''}} - 6 y^{^{'}} + 3 y = x e^{x}

What is the solution for x^{''}+x=tan(t) ?
The solution for x^{''}+x=tan(t) is x=c_{1}cos(t)+c_{2}sin(t)-cos(t)ln(tan(t)+sec(t))