What is the solution for (d^2+4)y=cos(x) ?

The solution for (d^2+4)y=cos(x) is y=c_{1}cos(2x)+c_{2}sin(2x)+1/3 cos(x)

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(d^2+4)y=cos(x)

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{3} cos (x)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{3} cos (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{3} cos (x)

y^{^{''}} + 2 y^{^{'}} - 15 y = 7 e^{3 t} + (1 - 2 t) sin (6 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = g (t), y (0) = 8, y^{^{'}} (0) = 6

y^{^{''}} - 4 y = 1, y^{^{'}} (0) = 2

y^{^{''}} - 16 y = 19.2 e^{4 x} + 60 e^{x}

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 (cos^{2} (x)) e^{x}

What is the solution for (d^2+4)y=cos(x) ?
The solution for (d^2+4)y=cos(x) is y=c_{1}cos(2x)+c_{2}sin(2x)+1/3 cos(x)