What is the solution for y^{''}+19y=4e^{8x} ?

The solution for y^{''}+19y=4e^{8x} is y=c_{1}cos(sqrt(19)x)+c_{2}sin(sqrt(19)x)+4/83 e^{8x}

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y^{''}+19y=4e^{8x}

y^{^{''}} + 19 y = 4 e^{8 x}

y = c_{1} cos (19 x) + c_{2} sin (19 x) + \frac{4}{83} e^{8 x}

Solution steps

y^{''} (x) + 19 y = 4 e^{8 x}

Solve linear ODE:

y = c_{1} cos (19 x) + c_{2} sin (19 x) + \frac{4}{83} e^{8 x}

y = c_{1} cos (19 x) + c_{2} sin (19 x) + \frac{4}{83} e^{8 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{3 x}

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

y^{^{''}} - 8 y^{^{'}} - 9 y = 21 e^{2} t

y^{^{''}} + 4 y^{^{'}} = 3 \cdot sin (2 x)

y^{^{''}} - 6 y^{^{'}} + 8 y = x e^{3 x} cos (4 x)

What is the solution for y^{''}+19y=4e^{8x} ?
The solution for y^{''}+19y=4e^{8x} is y=c_{1}cos(sqrt(19)x)+c_{2}sin(sqrt(19)x)+4/83 e^{8x}