What is the solution for (D^2+1)y=sec^2(x) ?

The solution for (D^2+1)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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(D^2+1)y=sec^2(x)

(D^{2} + 1) y = sec^{2} (x)

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

Solution steps

(D^{2} + 1) 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^{^{''}} + 2 y^{^{'}} + y = e^{- t} 1 + t

y^{^{''}} - 4 y^{^{'}} + 4 y = cos (2 x)

2 y^{^{''}} - y^{^{'}} - 3 y = 3 x e^{2 x}

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

D (D + 3) y = x (5 + e^{x})

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