What is the solution for y^{''}-6y^'+9y=15x+3 ?

The solution for y^{''}-6y^'+9y=15x+3 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+13/9

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y^{''}-6y^'+9y=15x+3

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 3

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{13}{9}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 15 x + 3

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{13}{9}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{13}{9}

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

\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}

What is the solution for y^{''}-6y^'+9y=15x+3 ?
The solution for y^{''}-6y^'+9y=15x+3 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+13/9