y^{''}+2y^'+y=4000sec(40x)

Lösung

y^{^{''}} + 2 y^{^{'}} + y = 4000 sec (40 x)

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{- x} \cdot \int - 4000 e^{x} x sec (40 x) d x + e^{- x} x \cdot \int 4000 e^{x} sec (40 x) d x

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + y = 4000 sec (40 x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{- x} \cdot \int - 4000 e^{x} x sec (40 x) d x + e^{- x} x \cdot \int 4000 e^{x} sec (40 x) d x

y = c_{1} e^{- x} + c_{2} x e^{- x} + e^{- x} \cdot \int - 4000 e^{x} x sec (40 x) d x + e^{- x} x \cdot \int 4000 e^{x} sec (40 x) d x

a x^{^{''}} + b x^{^{'}} + c = 0

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 10 y = 4 e^{5 t}

y^{^{''}} - y^{^{'}} - 12 y = e^{2} x + e^{x} - 2

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}, y (0) = - 2, y^{^{'}} (0) = 4

y^{^{''}} + y^{^{'}} - 12 y = \frac{e ^{x}}{x}