What is the solution for y^{''}+9y=5sin(3x),y(0)=6,y^'(0)=0 ?

The solution for y^{''}+9y=5sin(3x),y(0)=6,y^'(0)=0 is y=6cos(3x)+5/18 sin(3x)-(5xcos(3x))/6

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y^{''}+9y=5sin(3x),y(0)=6,y^'(0)=0

y^{^{''}} + 9 y = 5 sin (3 x), y (0) = 6, y^{^{'}} (0) = 0

y = 6 cos (3 x) + \frac{5}{18} sin (3 x) - \frac{5 x cos ( 3 x )}{6}

Solution steps

y^{''} (x) + 9 y = 5 sin (3 x)

Solve linear ODE:

y = 6 cos (3 x) + \frac{5}{18} sin (3 x) - \frac{5 x cos ( 3 x )}{6}

y = 6 cos (3 x) + \frac{5}{18} sin (3 x) - \frac{5 x cos ( 3 x )}{6}

What is the solution for y^{''}+9y=5sin(3x),y(0)=6,y^'(0)=0 ?
The solution for y^{''}+9y=5sin(3x),y(0)=6,y^'(0)=0 is y=6cos(3x)+5/18 sin(3x)-(5xcos(3x))/6