What is the solution for y^{''}+y= 1/(cos(t)) ?

The solution for y^{''}+y= 1/(cos(t)) is y=c_{1}cos(t)+c_{2}sin(t)+ln(cos(t))cos(t)+tsin(t)

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y^{''}+y= 1/(cos(t))

y^{^{''}} + y = \frac{1}{cos ( t )}

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

Solution steps

y^{''} (t) + y = \frac{1}{cos ( t )}

Solve linear ODE:

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

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

x^{^{''}} + 7 x = t e^{3 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

y^{^{''}} + 6 y = - 294 x^{2} e^{6} x

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- 3 x}

y^{^{''}} - y^{^{'}} - 2 y = 1

What is the solution for y^{''}+y= 1/(cos(t)) ?
The solution for y^{''}+y= 1/(cos(t)) is y=c_{1}cos(t)+c_{2}sin(t)+ln(cos(t))cos(t)+tsin(t)