What is the solution for D^3y=e^{3x} ?

The solution for D^3y=e^{3x} is y=c_{1}+c_{2}x+c_{3}x^2+1/27 e^{3x}

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D^3y=e^{3x}

D^{3} y = e^{3 x}

y = c_{1} + c_{2} x + c_{3} x^{2} + \frac{1}{27} e^{3 x}

Solution steps

D^{3} y = e^{3 x}

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} x^{2} + \frac{1}{27} e^{3 x}

y = c_{1} + c_{2} x + c_{3} x^{2} + \frac{1}{27} e^{3 x}

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

y^{^{''}} + 4 y^{^{'}} - 2 y = \frac{1}{x ^{2} e ^{2 x}}

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

y^{^{''}} - y^{^{'}} + y = 4, y^{^{'}} (0) = - 1, y (0) = 4

y^{^{''}} + y - 2 y = 2 + 5 cos (x)

What is the solution for D^3y=e^{3x} ?
The solution for D^3y=e^{3x} is y=c_{1}+c_{2}x+c_{3}x^2+1/27 e^{3x}