(d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t}

Lösung

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + x = 3 cos (t)

y^{^{''}} - 18 y = tan (x)

y^{^{''}} + y = 1, 6 cos (t) y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y = 15 t, y (0) = - 15 t

2 \frac{d ^{2} y}{d x ^{2}} + 4 y^{^{'}} + 2 y = \frac{1}{e ^{x} ( x + 1 )}