What is the solution for y^{''}-5y^'+6y=g(t) ?

The solution for y^{''}-5y^'+6y=g(t) is y=c_{1}e^{3t}+c_{2}e^{2t}+(gt)/6+(5g)/(36)

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y^{''}-5y^'+6y=g(t)

y^{^{''}} - 5 y^{^{'}} + 6 y = g (t)

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

Solution steps

y^{''} (t) - 5 y^{'} (t) + 6 y = g (t)

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 6 y = 1 + e^{- x}

y^{^{''}} - 7 y^{^{'}} + 12 = 0

y^{^{''}} - 2 y^{^{'}} - 3 = 0

y^{^{''}} + 4 y^{^{'}} + 13 y = 5

What is the solution for y^{''}-5y^'+6y=g(t) ?
The solution for y^{''}-5y^'+6y=g(t) is y=c_{1}e^{3t}+c_{2}e^{2t}+(gt)/6+(5g)/(36)