What is the solution for y^{''}-5y^'+6y=g(x) ?

The solution for y^{''}-5y^'+6y=g(x) is y=c_{1}e^{3x}+c_{2}e^{2x}+(gx)/6+(5g)/(36)

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y^{''}-5y^'+6y=g(x)

y^{^{''}} - 5 y^{^{'}} + 6 y = g (x)

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{gx}{6} + \frac{5 g}{36}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = g (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{gx}{6} + \frac{5 g}{36}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{gx}{6} + \frac{5 g}{36}

y^{^{''}} - 12 y^{^{'}} + 35 y = 96 e^{t}

y^{^{''}} + y + 2 sin (x) = 0

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

(D^{2} + 1) y = e^{- x} + cos (x) + x^{3}

y^{^{''}} - 3 y^{^{'}} + y = x

What is the solution for y^{''}-5y^'+6y=g(x) ?
The solution for y^{''}-5y^'+6y=g(x) is y=c_{1}e^{3x}+c_{2}e^{2x}+(gx)/6+(5g)/(36)