y^{''}+10y^'+25y=100sinh(5x)

Lösung

y^{^{''}} + 10 y^{^{'}} + 25 y = 100 sinh (5 x)

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + e^{- 5 x} \cdot \int - 100 e^{5 x} x sinh (5 x) d x + 100 e^{- 5 x} x (\frac{1}{5} e^{5 x} sinh (5 x) - \frac{1}{10} (5 x + \frac{1}{2} e^{10 x}))

Schritte zur Lösung

y^{''} (x) + 10 y^{'} (x) + 25 y = 100 sinh (5 x)

Solve linear ODE:

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + e^{- 5 x} \cdot \int - 100 e^{5 x} x sinh (5 x) d x + 100 e^{- 5 x} x (\frac{1}{5} e^{5 x} sinh (5 x) - \frac{1}{10} (5 x + \frac{1}{2} e^{10 x}))

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + e^{- 5 x} \cdot \int - 100 e^{5 x} x sinh (5 x) d x + 100 e^{- 5 x} x (\frac{1}{5} e^{5 x} sinh (5 x) - \frac{1}{10} (5 x + \frac{1}{2} e^{10 x}))

y^{^{''}} + 2 y^{^{'}} + y = 9 e^{- t}

y^{^{''}} - y = x^{3} - x

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = e^{2 x}

y^{^{''}} + 4 y = 4 sec^{2} (x)

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