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

The solution for y^{''}-5y^'+6y=x^2+3x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(7x)/9+16/27

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

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

y^{^{''}} + 3 y^{^{'}} = 54 x

(D^{2} + 4 D + 5) y = 50 x + 13 e^{e x}

y^{^{''}} + 4 y^{^{'}} + 29 y = 2, y^{^{'}} (0) = 3

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 e^{4 x}

y^{^{''}} + 2 y^{^{'}} + 3 y = 5 sin (4 t), y (0) = 2, y^{^{'}} (0) = 1

What is the solution for y^{''}-5y^'+6y=x^2+3x ?
The solution for y^{''}-5y^'+6y=x^2+3x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(7x)/9+16/27