What is the solution for y^{''}-16y=sin(2x)-3cos(2x) ?

The solution for y^{''}-16y=sin(2x)-3cos(2x) is y=c_{1}e^{4x}+c_{2}e^{-4x}-1/20 sin(2x)+3/20 cos(2x)

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y^{''}-16y=sin(2x)-3cos(2x)

y^{^{''}} - 16 y = sin (2 x) - 3 cos (2 x)

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

Solution steps

y^{''} (x) - 16 y = sin (2 x) - 3 cos (2 x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} lo g_{e} (1 + x^{2})

y^{^{''}} - y^{^{'}} = e^{2 x} - 4 x

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} 1 + x

y^{^{''}} - 6 y^{^{'}} + 8 y = 64 x^{2}

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

What is the solution for y^{''}-16y=sin(2x)-3cos(2x) ?
The solution for y^{''}-16y=sin(2x)-3cos(2x) is y=c_{1}e^{4x}+c_{2}e^{-4x}-1/20 sin(2x)+3/20 cos(2x)