What is the solution for y^{''}+8y^'-9y=64x+1 ?

The solution for y^{''}+8y^'-9y=64x+1 is y=c_{1}e^x+c_{2}e^{-9x}-(64x)/9-521/81

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y^{''}+8y^'-9y=64x+1

y^{^{''}} + 8 y^{^{'}} - 9 y = 64 x + 1

y = c_{1} e^{x} + c_{2} e^{- 9 x} - \frac{64 x}{9} - \frac{521}{81}

Solution steps

y^{''} (x) + 8 y^{'} (x) - 9 y = 64 x + 1

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 9 x} - \frac{64 x}{9} - \frac{521}{81}

y = c_{1} e^{x} + c_{2} e^{- 9 x} - \frac{64 x}{9} - \frac{521}{81}

\frac{d ^{2} y}{d x ^{2}} + y = 3 e^{- 5 x}

y^{^{''}} - 2 y^{^{'}} + 5 y = cos (2 x)

y^{^{''}} - 6 y^{^{'}} + 13 y = e^{3 x} cos (2 x)

y = 5 \frac{d ^{2} x}{d y ^{2}} + 3 \frac{d x}{d y}

y^{^{''}} + 4 y = sin (2 t) + t

What is the solution for y^{''}+8y^'-9y=64x+1 ?
The solution for y^{''}+8y^'-9y=64x+1 is y=c_{1}e^x+c_{2}e^{-9x}-(64x)/9-521/81