y^{''}-ay=-c

Lösung

y^{^{''}} - a y = - c

y = c_{1} e^{a t} + c_{2} e^{- a t} + \frac{c}{a}

Schritte zur Lösung

y^{''} (t) - a y = - c

Solve linear ODE:

y = c_{1} e^{a t} + c_{2} e^{- a t} + \frac{c}{a}

y = c_{1} e^{a t} + c_{2} e^{- a t} + \frac{c}{a}

2 x^{^{''}} + 4 x^{^{'}} - 3 = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (2 t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- 2 t}, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 7 e^{8 x}

y^{^{'''}} + y^{^{'}} = ln (x)