What is the solution for y^{''}+49y=-5cos(7t+pi^3) ?

The solution for y^{''}+49y=-5cos(7t+pi^3) is y=c_{1}cos(7t)+c_{2}sin(7t)-(5tsin(7t+pi^3))/(14)

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y^{''}+49y=-5cos(7t+pi^3)

y^{^{''}} + 49 y = - 5 cos (7 t + π^{3})

y = c_{1} cos (7 t) + c_{2} sin (7 t) - \frac{5 t sin ( 7 t + π ^{3} )}{14}

Solution steps

y^{''} (t) + 49 y = - 5 cos (7 t + π^{3})

Solve linear ODE:

y = c_{1} cos (7 t) + c_{2} sin (7 t) - \frac{5 t sin ( 7 t + π ^{3} )}{14}

y = c_{1} cos (7 t) + c_{2} sin (7 t) - \frac{5 t sin ( 7 t + π ^{3} )}{14}

y^{^{''}} + b^{2} y = sin (b t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} - y^{^{'}} = 6 sin (t)

y^{^{''}} + 4 y^{^{'}} + 5 y = (e^{- 2 x}) sec (x)

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{- 2 x} + sin (x)

y^{^{''}} - 4 y^{^{'}} + 4 y = x e^{2 x} + 1

What is the solution for y^{''}+49y=-5cos(7t+pi^3) ?
The solution for y^{''}+49y=-5cos(7t+pi^3) is y=c_{1}cos(7t)+c_{2}sin(7t)-(5tsin(7t+pi^3))/(14)