What is the solution for (D^2-7D+6)y=e^{6x}+e^x ?

The solution for (D^2-7D+6)y=e^{6x}+e^x is y=c_{1}e^{6x}+c_{2}e^x+(e^{6x}x-e^xx)/5

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(D^2-7D+6)y=e^{6x}+e^x

(D^{2} - 7 D + 6) y = e^{6 x} + e^{x}

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{e ^{6 x} x - e ^{x} x}{5}

Solution steps

(D^{2} - 7 D + 6) y = e^{6 x} + e^{x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{e ^{6 x} x - e ^{x} x}{5}

y = c_{1} e^{6 x} + c_{2} e^{x} + \frac{e ^{6 x} x - e ^{x} x}{5}

\frac{d ^{2} y}{d x ^{2}} - y = 4 e^{x} cos (x)

y^{^{''}} - y^{^{'}} - 2 x = 4 x^{2}

y^{^{''}} + 2 y^{^{'}} + 4 y = 2 t - 3 cos (2 t)

3 y^{^{''}} - 9 y^{^{'}} = sin (2 x)

y^{^{''}} + 9 y = 3, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for (D^2-7D+6)y=e^{6x}+e^x ?
The solution for (D^2-7D+6)y=e^{6x}+e^x is y=c_{1}e^{6x}+c_{2}e^x+(e^{6x}x-e^xx)/5