(d^2y)/(dx^2)+8(dy)/(dx)+16y=e^{4x}

Lösung

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = e^{4 x}

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{1}{64} e^{4 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = e^{4 x}

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{1}{64} e^{4 x}

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{1}{64} e^{4 x}

y^{^{''}} + 16 y^{^{'}} + 10000 y = 400 sin (200 x)

y^{^{''}} + 4 y^{^{'}} = e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{- 2 e ^{2 t}}{t ^{2} + 1}

y^{^{''}} + 7 y^{^{'}} + 10 y = 100 sin (10 t)

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