What is the solution for (d^2-5d+6)*y=x ?

The solution for (d^2-5d+6)*y=x is y=c_{1}e^{3x}+c_{2}e^{2x}+x/6+5/36

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(d^2-5d+6)*y=x

(d^{2} - 5 d + 6) \cdot y = x

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{6} + \frac{5}{36}

Solution steps

(d^{2} - 5 d + 6) y = x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{6} + \frac{5}{36}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{6} + \frac{5}{36}

y^{^{''}} - 6 y^{^{'}} + 8 y = 16 x^{2} - 2

(d^{3} - 2 d^{2} - 5 d + 6) y = e^{4} x

(d^{3} - 4 d) y = 2 cosh^{2} (2 x)

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

(d^{4} - 2 d^{3} - 3 d^{2} + 4 d + 4) y = cos (3 x + 5) + (e^{3})^{x}

What is the solution for (d^2-5d+6)*y=x ?
The solution for (d^2-5d+6)*y=x is y=c_{1}e^{3x}+c_{2}e^{2x}+x/6+5/36