What is the solution for y^{''}+9y=3x,y(0)=1,y^'(0)=3 ?

The solution for y^{''}+9y=3x,y(0)=1,y^'(0)=3 is y=cos(3x)+8/9 sin(3x)+x/3

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y^{''}+9y=3x,y(0)=1,y^'(0)=3

y^{^{''}} + 9 y = 3 x, y (0) = 1, y^{^{'}} (0) = 3

y = cos (3 x) + \frac{8}{9} sin (3 x) + \frac{x}{3}

Solution steps

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

Solve linear ODE:

y = cos (3 x) + \frac{8}{9} sin (3 x) + \frac{x}{3}

y = cos (3 x) + \frac{8}{9} sin (3 x) + \frac{x}{3}

What is the solution for y^{''}+9y=3x,y(0)=1,y^'(0)=3 ?
The solution for y^{''}+9y=3x,y(0)=1,y^'(0)=3 is y=cos(3x)+8/9 sin(3x)+x/3