What is the solution for y^{''}+17y=e^{6x} ?

The solution for y^{''}+17y=e^{6x} is y=c_{1}cos(sqrt(17)x)+c_{2}sin(sqrt(17)x)+1/53 e^{6x}

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y^{''}+17y=e^{6x}

y^{^{''}} + 17 y = e^{6 x}

y = c_{1} cos (17 x) + c_{2} sin (17 x) + \frac{1}{53} e^{6 x}

Solution steps

y^{''} (x) + 17 y = e^{6 x}

Solve linear ODE:

y = c_{1} cos (17 x) + c_{2} sin (17 x) + \frac{1}{53} e^{6 x}

y = c_{1} cos (17 x) + c_{2} sin (17 x) + \frac{1}{53} e^{6 x}

y^{^{''}} - y = sin (t), y (0) = 1, y (0) = - 1

y^{^{''}} + y = 6 e^{- 2 x}, y (0) = 0, y^{^{'}} (0) = 0

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

y^{^{''}} + 16 y = g (t), y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{\frac{3}{2}} e^{x}

What is the solution for y^{''}+17y=e^{6x} ?
The solution for y^{''}+17y=e^{6x} is y=c_{1}cos(sqrt(17)x)+c_{2}sin(sqrt(17)x)+1/53 e^{6x}