What is the solution for 0.001y^{''}+10y=10cos(100x) ?

The solution for 0.001y^{''}+10y=10cos(100x) is y=c_{1}cos(100x)+c_{2}sin(100x)+50xsin(100x)

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0.001y^{''}+10y=10cos(100x)

0.001 y^{^{''}} + 10 y = 10 cos (100 x)

y = c_{1} cos (100 x) + c_{2} sin (100 x) + 50 x sin (100 x)

Solution steps

0.001 y^{''} (x) + 10 y = 10 cos (100 x)

Solve linear ODE:

y = c_{1} cos (100 x) + c_{2} sin (100 x) + 50 x sin (100 x)

y = c_{1} cos (100 x) + c_{2} sin (100 x) + 50 x sin (100 x)

y^{^{''}} + 2 y^{^{'}} + y = (1 + x) e^{- x}

(D^{2} - 2 D + 1) y = x sin (x)

y^{^{''}} + 4 y = sin (5 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = x^{2} + sin (x)

y^{^{''}} + 3 y^{^{'}} - 10 y = 3 e^{- 5 x}

What is the solution for 0.001y^{''}+10y=10cos(100x) ?
The solution for 0.001y^{''}+10y=10cos(100x) is y=c_{1}cos(100x)+c_{2}sin(100x)+50xsin(100x)