What is the solution for x^{''}+25x=cos(t) ?

The solution for x^{''}+25x=cos(t) is x=c_{1}cos(5t)+c_{2}sin(5t)+1/24 cos(t)

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x^{''}+25x=cos(t)

x^{^{''}} + 25 x = cos (t)

x = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{24} cos (t)

Solution steps

x^{''} (t) + 25 x = cos (t)

Solve linear ODE:

x = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{24} cos (t)

x = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{24} cos (t)

y^{^{''}} + 7 y^{^{'}} - 12 y = e^{3} x - 2 e^{x} - 5 x

y^{^{''}} - 4 y = t cos (2 t)

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

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (\frac{9}{4} x)

\frac{d ^{2} y}{d x ^{2}} + a y^{^{'}} = b

What is the solution for x^{''}+25x=cos(t) ?
The solution for x^{''}+25x=cos(t) is x=c_{1}cos(5t)+c_{2}sin(5t)+1/24 cos(t)