What is the solution for y^{''}-6y^'+8y=e^{ax} ?

The solution for y^{''}-6y^'+8y=e^{ax} is y=c_{1}e^{4x}+c_{2}e^{2x}+(e^{ax})/(a^2-6a+8)

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y^{''}-6y^'+8y=e^{ax}

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{a x}

y = c_{1} e^{4 x} + c_{2} e^{2 x} + \frac{e ^{a x}}{a ^{2} - 6 a + 8}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 8 y = e^{a x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} + \frac{e ^{a x}}{a ^{2} - 6 a + 8}

y = c_{1} e^{4 x} + c_{2} e^{2 x} + \frac{e ^{a x}}{a ^{2} - 6 a + 8}

25 y^{^{''}} - 10 y^{^{'}} - 2 y = 4 e^{t}

y^{^{''}} + 0.5 y^{^{'}} + y = cos (t)

y^{^{''}} + y = 2 cos (x), y (0) = 1, y^{^{'}} (0) = 0

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

(D + 1)^{3} y = 16 (2 x + 3)^{- 1} e^{x}

What is the solution for y^{''}-6y^'+8y=e^{ax} ?
The solution for y^{''}-6y^'+8y=e^{ax} is y=c_{1}e^{4x}+c_{2}e^{2x}+(e^{ax})/(a^2-6a+8)