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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 10 y = e^{3 x} cos (x)

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

y^{^{''}} - 4 y^{^{'}} - 21 y = 320 e^{- t}

6 y^{^{''}} - y^{^{'}} - y = 50 e^{\frac{x}{2}} + 4 x^{2} - 5

\frac{d ^{2} y}{d x ^{2}} + 5 y - sin (π x) = 0

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