What is the solution for 3y^{''}-12y^'+9y=3sin(4x) ?

The solution for 3y^{''}-12y^'+9y=3sin(4x) is y=c_{1}e^{3x}+c_{2}e^x-13/425 sin(4x)+16/425 cos(4x)

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3y^{''}-12y^'+9y=3sin(4x)

3 y^{^{''}} - 12 y^{^{'}} + 9 y = 3 sin (4 x)

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{13}{425} sin (4 x) + \frac{16}{425} cos (4 x)

Solution steps

3 y^{''} (x) - 12 y^{'} (x) + 9 y = 3 sin (4 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{13}{425} sin (4 x) + \frac{16}{425} cos (4 x)

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{13}{425} sin (4 x) + \frac{16}{425} cos (4 x)

x \to 1 lim (\frac{x}{( x - 1 ) ^{2}})

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

\int \frac{3}{64} x^{2} d x

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

x \to 0 lim (\frac{sin ( x ^{9} )}{x})

What is the solution for 3y^{''}-12y^'+9y=3sin(4x) ?
The solution for 3y^{''}-12y^'+9y=3sin(4x) is y=c_{1}e^{3x}+c_{2}e^x-13/425 sin(4x)+16/425 cos(4x)