What is the solution for 50x^{''}+10^6x=10 ?

The solution for 50x^{''}+10^6x=10 is x=c_{1}cos(100sqrt(2)t)+c_{2}sin(100sqrt(2)t)+1/100000

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50x^{''}+10^6x=10

50 x^{^{''}} + 1 0^{6} x = 10

x = c_{1} cos (1002 t) + c_{2} sin (1002 t) + \frac{1}{100000}

Solution steps

50 x^{''} (t) + 1 0^{6} x = 10

Solve linear ODE:

x = c_{1} cos (1002 t) + c_{2} sin (1002 t) + \frac{1}{100000}

x = c_{1} cos (1002 t) + c_{2} sin (1002 t) + \frac{1}{100000}

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 H (t)

y^{^{''}} + 9 y = 12 cos (3 t), y (0) = 0, y^{^{'}} (0) = 6

y^{^{''}} + 4 y^{^{'}} + 5 = 4 e^{- 2 t} tan (t)

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

y^{^{''}} - 2 y^{^{'}} = 3, y (0) = - 3 e^{- x}

What is the solution for 50x^{''}+10^6x=10 ?
The solution for 50x^{''}+10^6x=10 is x=c_{1}cos(100sqrt(2)t)+c_{2}sin(100sqrt(2)t)+1/100000