What is the solution for 16y^{''}+y=4sec(pi/4) ?

The solution for 16y^{''}+y=4sec(pi/4) is y=c_{1}cos(t/4)+c_{2}sin(t/4)+4sqrt(2)

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16y^{''}+y=4sec(pi/4)

16 y^{^{''}} + y = 4 sec (\frac{π}{4})

y = c_{1} cos (\frac{t}{4}) + c_{2} sin (\frac{t}{4}) + 42

Solution steps

16 y^{''} (t) + y = 4 sec (\frac{π}{4})

Solve linear ODE:

y = c_{1} cos (\frac{t}{4}) + c_{2} sin (\frac{t}{4}) + 42

y = c_{1} cos (\frac{t}{4}) + c_{2} sin (\frac{t}{4}) + 42

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

y^{^{''}} + y^{^{'}} - 8 y = 48 t

y^{^{''}} - 2 y^{^{'}} + 1 = x e^{x}

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 9 + 24 x + 4

What is the solution for 16y^{''}+y=4sec(pi/4) ?
The solution for 16y^{''}+y=4sec(pi/4) is y=c_{1}cos(t/4)+c_{2}sin(t/4)+4sqrt(2)