What is the solution for y^{''}+18y=3e^{8x} ?

The solution for y^{''}+18y=3e^{8x} is y=c_{1}cos(sqrt(2)*3x)+c_{2}sin(sqrt(2)*3x)+3/82 e^{8x}

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y^{''}+18y=3e^{8x}

y^{^{''}} + 18 y = 3 e^{8 x}

y = c_{1} cos (2 \cdot 3 x) + c_{2} sin (2 \cdot 3 x) + \frac{3}{82} e^{8 x}

Solution steps

y^{''} (x) + 18 y = 3 e^{8 x}

Solve linear ODE:

y = c_{1} cos (2 \cdot 3 x) + c_{2} sin (2 \cdot 3 x) + \frac{3}{82} e^{8 x}

y = c_{1} cos (2 \cdot 3 x) + c_{2} sin (2 \cdot 3 x) + \frac{3}{82} e^{8 x}

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

q^{^{''}} + 3 q^{^{'}} + 2 q = e^{- t} + e^{- 2 t}

y^{^{''}} - 14 y^{^{'}} + 40 y = 26 + 40 x

\frac{d ^{2} y}{d x ^{2}} - 4 y = 8 x^{2} - x + 12

y^{^{'''}} + 5 y^{^{''}} - 14 = 0

What is the solution for y^{''}+18y=3e^{8x} ?
The solution for y^{''}+18y=3e^{8x} is y=c_{1}cos(sqrt(2)*3x)+c_{2}sin(sqrt(2)*3x)+3/82 e^{8x}