What is the solution for y^{''}-3y^'=cos(5x),y(0)=0,y^'(0)=0 ?

The solution for y^{''}-3y^'=cos(5x),y(0)=0,y^'(0)=0 is y= 1/34 e^{3x}-3/170 sin(5x)-1/34 cos(5x)

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y^{''}-3y^'=cos(5x),y(0)=0,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} = cos (5 x), y (0) = 0, y^{^{'}} (0) = 0

y = \frac{1}{34} e^{3 x} - \frac{3}{170} sin (5 x) - \frac{1}{34} cos (5 x)

Solution steps

y^{''} (x) - 3 y^{'} (x) = cos (5 x)

Solve linear ODE:

y = \frac{1}{34} e^{3 x} - \frac{3}{170} sin (5 x) - \frac{1}{34} cos (5 x)

y = \frac{1}{34} e^{3 x} - \frac{3}{170} sin (5 x) - \frac{1}{34} cos (5 x)

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{3} e^{3 t}

2 y^{^{'''}} - 2 y^{^{'}} = - 3 t^{2} - 4 t

y^{^{''}} + 2 y^{^{'}} + 392 y = cos (2 t)

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 3 t^{2} - 18

y^{^{''}} + 8 y^{^{'}} + 2 y = cos (x), y (0) = 0

What is the solution for y^{''}-3y^'=cos(5x),y(0)=0,y^'(0)=0 ?
The solution for y^{''}-3y^'=cos(5x),y(0)=0,y^'(0)=0 is y= 1/34 e^{3x}-3/170 sin(5x)-1/34 cos(5x)