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Popular >

y^'-10^{-3}y=220cos(50x)

Solution

y^{^{'}} - 1 0^{- 3} y = 220 cos (50 x)

Solution

y = 220 e^{\frac{x}{1000}} (- \frac{1000}{2500000001} e^{- \frac{x}{1000}} cos (50 x) - \frac{1}{125000000050} e^{- \frac{x}{1000}} sin (50 x) + \frac{1}{50} e^{- \frac{1}{1000} x} sin (50 x)) + c_{1} e^{\frac{1}{1000} x}

Solution steps

y^{'} (x) - 1 0^{- 3} y = 220 cos (50 x)

Solve linear ODE:

y = 220 e^{\frac{x}{1000}} (- \frac{1000}{2500000001} e^{- \frac{x}{1000}} cos (50 x) - \frac{1}{125000000050} e^{- \frac{x}{1000}} sin (50 x) + \frac{1}{50} e^{- \frac{1}{1000} x} sin (50 x)) + c_{1} e^{\frac{1}{1000} x}

y = 220 e^{\frac{x}{1000}} (- \frac{1000}{2500000001} e^{- \frac{x}{1000}} cos (50 x) - \frac{1}{125000000050} e^{- \frac{x}{1000}} sin (50 x) + \frac{1}{50} e^{- \frac{1}{1000} x} sin (50 x)) + c_{1} e^{\frac{1}{1000} x}

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Frequently Asked Questions (FAQ)

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