What is the solution for y^{''}-6y^'+9y=15x+4 ?

The solution for y^{''}-6y^'+9y=15x+4 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+14/9

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y^{''}-6y^'+9y=15x+4

y^{^{''}} - 6 y^{^{'}} + 9 y = 15 x + 4

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{14}{9}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 15 x + 4

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{14}{9}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{14}{9}

y^{^{''}} + y = 2 x \cdot e^{x} - 2 sin (x)

y^{^{''}} - y = 2 ln (x)

y^{^{''}} - 2 y^{^{'}} + y = 25 cos (2 x)

\frac{d ^{2} y}{d x ^{2}} = a y + b

y^{^{''}} + 6 y^{^{'}} + 5 y = 10 cos (5 t)

What is the solution for y^{''}-6y^'+9y=15x+4 ?
The solution for y^{''}-6y^'+9y=15x+4 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+14/9