What is the solution for y^{''}-6y^'+9y=15x+2 ?

The solution for y^{''}-6y^'+9y=15x+2 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+4/3

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y^{''}-6y^'+9y=15x+2

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 2

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{4}{3}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 15 x + 2

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{4}{3}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{4}{3}

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 15 = 0

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

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

What is the solution for y^{''}-6y^'+9y=15x+2 ?
The solution for y^{''}-6y^'+9y=15x+2 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+4/3