What is the solution for y^{''}-6y^'+9y=9x+4 ?

The solution for y^{''}-6y^'+9y=9x+4 is y=c_{1}e^{3x}+c_{2}xe^{3x}+x+10/9

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y^{''}-6y^'+9y=9x+4

y^{^{''}} - 6 y^{^{'}} + 9 y = 9 x + 4

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + x + \frac{10}{9}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 9 x + 4

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + x + \frac{10}{9}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + x + \frac{10}{9}

x^{^{''}} - 25 x = t^{2} + t

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

4 y^{^{''}} - 4 y^{^{'}} + y = 48 e^{\frac{t}{2}}

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

y^{^{''}} - y = 5 sin (2 t)

What is the solution for y^{''}-6y^'+9y=9x+4 ?
The solution for y^{''}-6y^'+9y=9x+4 is y=c_{1}e^{3x}+c_{2}xe^{3x}+x+10/9