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

The solution for y^{''}-6y^'+9y=15x+6 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+16/9

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

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

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{16}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{16}{9}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{5 x}{3} + \frac{16}{9}

What is the solution for y^{''}-6y^'+9y=15x+6 ?
The solution for y^{''}-6y^'+9y=15x+6 is y=c_{1}e^{3x}+c_{2}xe^{3x}+(5x)/3+16/9