What is the solution for y^{''}-5y^'+6y=2x+3e^{8x} ?

The solution for y^{''}-5y^'+6y=2x+3e^{8x} is y=c_{1}e^{3x}+c_{2}e^{2x}+x/3+5/18+1/10 e^{8x}

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y^{''}-5y^'+6y=2x+3e^{8x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x + 3 e^{8 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{3} + \frac{5}{18} + \frac{1}{10} e^{8 x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 2 x + 3 e^{8 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{3} + \frac{5}{18} + \frac{1}{10} e^{8 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{3} + \frac{5}{18} + \frac{1}{10} e^{8 x}

y^{^{''}} - 6 y^{^{'}} + 8 y = 2 x - 1

y^{^{''}} + 2 y^{^{'}} - 3 y = x^{2} e^{x}

(d^{2} + d + 1) y = e^{x}

3 \frac{d ^{2} x}{d t ^{2}} + 60 x = 2 cos (25 t)

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 = 0

What is the solution for y^{''}-5y^'+6y=2x+3e^{8x} ?
The solution for y^{''}-5y^'+6y=2x+3e^{8x} is y=c_{1}e^{3x}+c_{2}e^{2x}+x/3+5/18+1/10 e^{8x}