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

The solution for y^{''}-5y^'+6y=3x^2+5x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/2+(5x)/3+11/9

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

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{2} + \frac{5 x}{3} + \frac{11}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{2} + \frac{5 x}{3} + \frac{11}{9}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{2} + \frac{5 x}{3} + \frac{11}{9}

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 0, y^{^{'}} (0) = a

y^{^{''}} + 4 y = sin^{22} (x)

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

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

6 y^{^{''}} + 4 y^{^{'}} - y = 25

What is the solution for y^{''}-5y^'+6y=3x^2+5x ?
The solution for y^{''}-5y^'+6y=3x^2+5x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/2+(5x)/3+11/9