What is the solution for y^{''}-7y^'+6y=(20x+11)e^x ?

The solution for y^{''}-7y^'+6y=(20x+11)e^x is y=c_{1}e^{6x}+c_{2}e^x-2x^2e^x-3e^xx

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y^{''}-7y^'+6y=(20x+11)e^x

y^{^{''}} - 7 y^{^{'}} + 6 y = (20 x + 11) e^{x}

y = c_{1} e^{6 x} + c_{2} e^{x} - 2 x^{2} e^{x} - 3 e^{x} x

Solution steps

y^{''} (x) - 7 y^{'} (x) + 6 y = (20 x + 11) e^{x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{x} - 2 x^{2} e^{x} - 3 e^{x} x

y = c_{1} e^{6 x} + c_{2} e^{x} - 2 x^{2} e^{x} - 3 e^{x} x

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 7 + e^{\frac{x}{2}}

V^{^{''}} + 25 \cdot 1 0^{2} V^{^{'}} + 25 \cdot 1 0^{6} V = 5 \cdot 1 0^{8}

y^{^{''}} + 49 y = 6 cos (7 x) + 9 sin (7 x)

3 y^{^{''}} - 6 y^{^{'}} + 30 y = 15 sin (x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e^{x} cos (5 x)

What is the solution for y^{''}-7y^'+6y=(20x+11)e^x ?
The solution for y^{''}-7y^'+6y=(20x+11)e^x is y=c_{1}e^{6x}+c_{2}e^x-2x^2e^x-3e^xx