What is the solution for y^{''}-4y^'+3y=9x^2-36x+37 ?

The solution for y^{''}-4y^'+3y=9x^2-36x+37 is y=c_{1}e^{3x}+c_{2}e^x+3x^2-4x+5

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y^{''}-4y^'+3y=9x^2-36x+37

y^{^{''}} - 4 y^{^{'}} + 3 y = 9 x^{2} - 36 x + 37

y = c_{1} e^{3 x} + c_{2} e^{x} + 3 x^{2} - 4 x + 5

Solution steps

y^{''} (x) - 4 y^{'} (x) + 3 y = 9 x^{2} - 36 x + 37

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} + 3 x^{2} - 4 x + 5

y = c_{1} e^{3 x} + c_{2} e^{x} + 3 x^{2} - 4 x + 5

y^{^{''}} + 3 y^{^{'}} = 2 x^{4} + x^{2} e^{- 3 x} + sin (3 x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 1 + t, y (0) = 0, y^{^{'}} (0) = 4

x^{^{''}} + 4 x^{^{'}} + 5 x = 13 sin (2 t)

y^{^{''}} - 3 y^{^{'}} + 4 y = 16 x - 12 e^{2 x}

y^{^{''}} - 7 y^{^{'}} = (x - 1)^{2}

What is the solution for y^{''}-4y^'+3y=9x^2-36x+37 ?
The solution for y^{''}-4y^'+3y=9x^2-36x+37 is y=c_{1}e^{3x}+c_{2}e^x+3x^2-4x+5