What is the solution for y^{''}+36y=2e^{6x} ?

The solution for y^{''}+36y=2e^{6x} is y=c_{1}cos(6x)+c_{2}sin(6x)+1/36 e^{6x}

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y^{''}+36y=2e^{6x}

y^{^{''}} + 36 y = 2 e^{6 x}

y = c_{1} cos (6 x) + c_{2} sin (6 x) + \frac{1}{36} e^{6 x}

Solution steps

y^{''} (x) + 36 y = 2 e^{6 x}

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) + \frac{1}{36} e^{6 x}

y = c_{1} cos (6 x) + c_{2} sin (6 x) + \frac{1}{36} e^{6 x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{4 t}

d (x) = \frac{3}{2 x}

(d^{2} + 6 d + 9) y = \frac{e ^{- 3} x}{x ^{3}}

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

x^{^{''}} + 16 x = 36 cos (2 t)

What is the solution for y^{''}+36y=2e^{6x} ?
The solution for y^{''}+36y=2e^{6x} is y=c_{1}cos(6x)+c_{2}sin(6x)+1/36 e^{6x}