y^'-ky=a+be^{-kt},y(0)=0

Lösung

y^{^{'}} - k y = a + b e^{- k t}, y (0) = 0

y = - \frac{a}{k} - \frac{b}{2 k e ^{k t}} + (\frac{a}{k} + \frac{b}{2 k}) e^{k t}

Schritte zur Lösung

y^{'} (t) - k y = a + b e^{- k t}

Solve linear ODE:

y = - \frac{a}{k} - \frac{b}{2 k e ^{k t}} + (\frac{a}{k} + \frac{b}{2 k}) e^{k t}

y = - \frac{a}{k} - \frac{b}{2 k e ^{k t}} + (\frac{a}{k} + \frac{b}{2 k}) e^{k t}

\int (- 7 sec (x) tan (x) + 8 sec^{2} (x)) d x

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