What is the solution for y^{''}-14y^'+45y=360x^2-224x+16 ?

The solution for y^{''}-14y^'+45y=360x^2-224x+16 is y=c_{1}e^{9x}+c_{2}e^{5x}+8x^2

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y^{''}-14y^'+45y=360x^2-224x+16

y^{^{''}} - 14 y^{^{'}} + 45 y = 360 x^{2} - 224 x + 16

y = c_{1} e^{9 x} + c_{2} e^{5 x} + 8 x^{2}

Solution steps

y^{''} (x) - 14 y^{'} (x) + 45 y = 360 x^{2} - 224 x + 16

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{5 x} + 8 x^{2}

y = c_{1} e^{9 x} + c_{2} e^{5 x} + 8 x^{2}

y^{^{''}} + 4 y = 4 cos (2 x) + 6 cos (x)

y^{^{''}} + 5 y^{^{'}} + 4 y = sec (x)

y^{^{''}} + 4 y = cos (t), y^{^{'}} (0) = 1, y (0) = 1

y^{^{''}} - 4 y = (x + 1) \cdot e^{x}

y^{^{''}} - 4 y = 16 x^{3}, y (0) = 2, y^{^{'}} (0) = - 14

What is the solution for y^{''}-14y^'+45y=360x^2-224x+16 ?
The solution for y^{''}-14y^'+45y=360x^2-224x+16 is y=c_{1}e^{9x}+c_{2}e^{5x}+8x^2