What is the solution for y^{''}+5y=(x) ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} - y^{^{'}} = 8 - (t - 2)

x^{^{''}} - 16 x^{^{'}} + 64 x = 5 t e^{8 t}

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 x + 1

0.05 y^{^{''}} + 5 y^{^{'}} + \frac{1}{0.006} y = 5 sin (25 x)

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