What is the solution for y^{''}+y=sec^2(t) ?

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

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y^{''}+y=sec^2(t)

y^{^{''}} + y = sec^{2} (t)

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

Solution steps

y^{''} (t) + y = sec^{2} (t)

Solve linear ODE:

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

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

y^{^{''}} - 12 y^{^{'}} + 36 y = 6 e^{6 x}

y^{^{'''}} - y^{^{'}} = 3 cos (x)

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

y^{^{''}} + y = g (t), y (0) = 0, y^{^{'}} (0) = 4

y^{^{''}} + 4 y = \frac{e ^{2 x}}{x}

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