What is the solution for (d^2+d+1)y=e^x ?

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

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(d^2+d+1)y=e^x

(d^{2} + d + 1) y = e^{x}

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

Solution steps

(d^{2} + d + 1) y = e^{x}

Solve linear ODE:

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

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

3 \frac{d ^{2} x}{d t ^{2}} + 60 x = 2 cos (25 t)

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 = 0

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 6 e x + 10 cos (x)

y^{^{''}} = 2 y + 22 cot^{3} (x), y (0) = 11 cot (x)

2 y^{^{''}} + 18 y + 5 = 0, y (0) = 0, y^{^{'}} (0) = 0

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