What is the solution for y^{''}-17y^'+72y=55+72x ?

The solution for y^{''}-17y^'+72y=55+72x is y=c_{1}e^{9x}+c_{2}e^{8x}+x+1

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y^{''}-17y^'+72y=55+72x

y^{^{''}} - 17 y^{^{'}} + 72 y = 55 + 72 x

y = c_{1} e^{9 x} + c_{2} e^{8 x} + x + 1

Solution steps

y^{''} (x) - 17 y^{'} (x) + 72 y = 55 + 72 x

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{8 x} + x + 1

y = c_{1} e^{9 x} + c_{2} e^{8 x} + x + 1

y^{^{''}} - y^{^{'}} - 6 y = 5 e^{2 x}

y^{^{''}} + 2 y^{^{'}} + 7 y = 6 cos (2 x)

y^{^{'''}} + 16 y^{^{'}} = sec (4 x)

(D^{2} - 4 D + 3) y = e^{3 x} cos (2 x)

y^{^{''}} - 5 y^{^{'}} = 8 e^{4} t - 4 e - t, y (0) = 1, y^{^{'}} (0) = - 1

What is the solution for y^{''}-17y^'+72y=55+72x ?
The solution for y^{''}-17y^'+72y=55+72x is y=c_{1}e^{9x}+c_{2}e^{8x}+x+1