x^{''}+16x=102e^{-2t}cos(4t)

Lösung

x^{^{''}} + 16 x = 102 e^{- 2 t} cos (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) - 6 e^{- 2 t} sin (4 t) + \frac{3}{2} e^{- 2 t} cos (4 t)

Schritte zur Lösung

x^{''} (t) + 16 x = 102 e^{- 2 t} cos (4 t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) - 6 e^{- 2 t} sin (4 t) + \frac{3}{2} e^{- 2 t} cos (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) - 6 e^{- 2 t} sin (4 t) + \frac{3}{2} e^{- 2 t} cos (4 t)

y^{^{''}} - y = 6 t + 1

y^{^{''}} - y = 6 t + 8

\frac{d ^{2} y}{d t ^{2}} + y = e^{- 2 t} sin (t)

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

y^{^{''}} - 2 y + 1 = 3 e^{x}