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

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

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y^{'''}+y^'=cos(x)

y^{^{'''}} + y^{^{'}} = cos (x)

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

Solution steps

y^{'''} (x) + y^{'} (x) = cos (x)

Solve linear ODE:

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

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

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