What is the solution for 4y^{''}+y=10cos(x) ?

The solution for 4y^{''}+y=10cos(x) is y=c_{1}cos(x/2)+c_{2}sin(x/2)-10/3 cos(x)

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4y^{''}+y=10cos(x)

4 y^{^{''}} + y = 10 cos (x)

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) - \frac{10}{3} cos (x)

Solution steps

4 y^{''} (x) + y = 10 cos (x)

Solve linear ODE:

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) - \frac{10}{3} cos (x)

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) - \frac{10}{3} cos (x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 8 e^{- 2} x

y^{^{''}} + 3 y^{^{'}} + 2 y = 2 x + 3

y^{^{''}} - 3 y^{^{'}} - 4 y = 2 sin (x) + 4 x^{2}

y^{^{''}} + 2 y^{^{'}} - 3 y = 3 x^{2} - 4 x

y^{^{''}} + 9 y = 18 x + 36 sin (3 x)

What is the solution for 4y^{''}+y=10cos(x) ?
The solution for 4y^{''}+y=10cos(x) is y=c_{1}cos(x/2)+c_{2}sin(x/2)-10/3 cos(x)