What is the solution for x^{''}+8x^'+16x=10sin(4t) ?

The solution for x^{''}+8x^'+16x=10sin(4t) is x=c_{1}e^{-4t}+c_{2}te^{-4t}-5/16 cos(4t)

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x^{''}+8x^'+16x=10sin(4t)

x^{^{''}} + 8 x^{^{'}} + 16 x = 10 sin (4 t)

x = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{5}{16} cos (4 t)

Solution steps

x^{''} (t) + 8 x^{'} (t) + 16 x = 10 sin (4 t)

Solve linear ODE:

x = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{5}{16} cos (4 t)

x = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} - \frac{5}{16} cos (4 t)

y^{^{''}} - 7 y^{^{'}} + 12 y = 6 e^{x}

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 x^{2} + x - 2

y^{^{''}} - 4 y = 8 x^{3}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + a y^{^{'}} + b y = sin (x) + 1

y^{^{''}} - y^{^{'}} - 6 y = 5 cos (3 x)

What is the solution for x^{''}+8x^'+16x=10sin(4t) ?
The solution for x^{''}+8x^'+16x=10sin(4t) is x=c_{1}e^{-4t}+c_{2}te^{-4t}-5/16 cos(4t)