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

The solution for y^{''}-5y^'+6y=x^2 is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(5x)/(18)+19/108

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

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{5 x}{18} + \frac{19}{108}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{5 x}{18} + \frac{19}{108}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{5 x}{18} + \frac{19}{108}

y^{^{''}} - 4 y^{^{'}} - 12 y = 2 x + 6

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} e^{- 2 x} + 1

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 6

What is the solution for y^{''}-5y^'+6y=x^2 ?
The solution for y^{''}-5y^'+6y=x^2 is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(5x)/(18)+19/108