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Beliebt Rechnen >

x^{''}-12x^'+36x=2t+e^{6t}

Lösung

x^{^{''}} - 12 x^{^{'}} + 36 x = 2 t + e^{6 t}

Lösung

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

Schritte zur Lösung

x^{''} (t) - 12 x^{'} (t) + 36 x = 2 t + e^{6 t}

Solve linear ODE:

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

Graph

Beliebte Beispiele

4y^{''}-y=(ex)/(2+5)

y^{''}+2y^'+2y=4e^{-x}cos(x)

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

y^{''}+3y^'+2y=e^{2x}cos(x)