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Beliebt Rechnen >

y^{''}-4y^'-12y=3e^5t

Lösung

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 e^{5} t

Lösung

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{e ^{5} t}{4} + \frac{e ^{5}}{12}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 12 y = 3 e^{5} t

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{e ^{5} t}{4} + \frac{e ^{5}}{12}

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{e ^{5} t}{4} + \frac{e ^{5}}{12}

Graph

Beliebte Beispiele

y^{'''}-4y^{''}-y^'+4y=e^{6x}

y^{^{'''}} - 4 y^{^{''}} - y^{^{'}} + 4 y = e^{6 x}

y^{''}-4y^'+5y=12e^t,y(0)=6,y^'(0)=7

y^{^{''}} - 4 y^{^{'}} + 5 y = 12 e^{t}, y (0) = 6, y^{^{'}} (0) = 7

(D^2-D-2)y=3e^{2x}

(D^{2} - D - 2) y = 3 e^{2 x}

(d^2y)/(dt^2)-3(dy)/(dt)-18y=(t+1)e^t

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 18 y = (t + 1) e^{t}

y^{^{''}} + y = H (t)