What is the solution for y^{''}+3y=6x ?

The solution for y^{''}+3y=6x is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)+2x

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y^{''}+3y=6x

y^{^{''}} + 3 y = 6 x

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x

Solution steps

y^{''} (x) + 3 y = 6 x

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x

y^{^{''}} - 3 y^{^{'}} + 2 = 0

- 2 y^{^{''}} + 7 y^{^{'}} - y - 8 = - 6 x^{2} - 2 x^{3} e^{x}

y^{^{''}} - y^{^{'}} - 2 y = 4 t^{2}

\frac{d ^{2} y}{d x ^{2}} + 25 y = 5 x^{2} + x

25 y^{^{''}} - 9 y = sin (x)

What is the solution for y^{''}+3y=6x ?
The solution for y^{''}+3y=6x is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)+2x