What is the solution for y^{''}+3y=x^3+1 ?

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

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y^{''}+3y=x^3+1

y^{^{''}} + 3 y = x^{3} + 1

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

Solution steps

y^{''} (x) + 3 y = x^{3} + 1

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} - 4 t + 4 = 0, y (0) = 2, y^{^{'}} (0) = 9

y^{^{''}} - 5 y^{^{'}} + 6 y = 5 \cdot e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = 2 cos (3 x)

2 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 6 y = 14 e^{x}

\frac{1}{4} y^{^{''}} + 2 y^{^{'}} + 40 y = - \frac{20}{3} t - \frac{4}{3}

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