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

The solution for y^{''}+9y=cos(3x)+sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+(xsin(3x))/6-(xcos(3x))/6

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y^{''}+9y=cos(3x)+sin(3x)

y^{^{''}} + 9 y = cos (3 x) + sin (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{x sin ( 3 x )}{6} - \frac{x cos ( 3 x )}{6}

Solution steps

y^{''} (x) + 9 y = cos (3 x) + sin (3 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{x sin ( 3 x )}{6} - \frac{x cos ( 3 x )}{6}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{x sin ( 3 x )}{6} - \frac{x cos ( 3 x )}{6}

y^{^{'}} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

2 x^{3} + 2 x - 1

z \to - 1 + 2 i lim (\frac{z}{z + 1 + 2 i})

\frac{d}{d x} (- \frac{x ^{2}}{y ^{2}})

m \to 0 lim (\frac{m}{m ^{2} + 4 m})

What is the solution for y^{''}+9y=cos(3x)+sin(3x) ?
The solution for y^{''}+9y=cos(3x)+sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+(xsin(3x))/6-(xcos(3x))/6