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

Lösung

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

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{- x} \cdot \int - e^{x} x sec^{2} (x) d x + e^{- x} x \cdot \int e^{x} sec^{2} (x) d x

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{- x} \cdot \int - e^{x} x sec^{2} (x) d x + e^{- x} x \cdot \int e^{x} sec^{2} (x) d x

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{- x} \cdot \int - e^{x} x sec^{2} (x) d x + e^{- x} x \cdot \int e^{x} sec^{2} (x) d x

3 x^{^{''}} + 48 x = 153 e^{- 2 t} cos (4 t)

y^{^{''}} - 9 y = 4 e^{3 t}, y (0) = 0, y^{^{'}} (0) = - 1

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 cos^{2} (4 x)

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} = 2 - 24 e^{x} + 40 e^{5 x}

y^{^{''}} + 2 y = cos (2) t + sin (2) t