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Beliebt Rechnen >

x^{''}-8x^'+16x=3te^{4t}

Lösung

x^{^{''}} - 8 x^{^{'}} + 16 x = 3 t e^{4 t}

Lösung

x = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t} t ^{3}}{2}

Schritte zur Lösung

x^{''} (t) - 8 x^{'} (t) + 16 x = 3 t e^{4 t}

Solve linear ODE:

x = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t} t ^{3}}{2}

x = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t} t ^{3}}{2}

Graph

Beliebte Beispiele

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

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

y^{''}+3y^'+7y=cos(t),y(0)=0,y^'(0)=2

y^{^{''}} + 3 y^{^{'}} + 7 y = cos (t), y (0) = 0, y^{^{'}} (0) = 2

y^{''}+3y^'-4y=2,y(0)=0,y(0)=0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y (0) = 0

4y^{''}+4y^'+1=0

4 y^{^{''}} + 4 y^{^{'}} + 1 = 0

D (x) = a - 2