What is the solution for 5y^{''}+y=-6x ?

The solution for 5y^{''}+y=-6x is y=c_{1}cos(x/(sqrt(5)))+c_{2}sin(x/(sqrt(5)))-6x

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5y^{''}+y=-6x

5 y^{^{''}} + y = - 6 x

y = c_{1} cos (\frac{x}{5}) + c_{2} sin (\frac{x}{5}) - 6 x

Solution steps

5 y^{''} (x) + y = - 6 x

Solve linear ODE:

y = c_{1} cos (\frac{x}{5}) + c_{2} sin (\frac{x}{5}) - 6 x

y = c_{1} cos (\frac{x}{5}) + c_{2} sin (\frac{x}{5}) - 6 x

y^{^{''}} + 25 y = cos (5 x)

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

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}

y^{^{''}} + 4 y = 4 cos (2 x) + 6 cos (x) + 8 x^{2} - 4 x

y^{^{''}} - 4 y^{^{'}} + 3 y = 20 cos (x)

What is the solution for 5y^{''}+y=-6x ?
The solution for 5y^{''}+y=-6x is y=c_{1}cos(x/(sqrt(5)))+c_{2}sin(x/(sqrt(5)))-6x